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Motion Test - 17

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Motion Test - 17
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  • Question 1
    1 / -0

    A bus starts from rest and travels with a uniform acceleration of 2.5 m/s2. What will be its velocity after eight seconds?

    Solution

    Initial velocity of the bus, u = 0 (Since it starts from rest)

    Acceleration, a = 2.5 m/s2

    Time, t = 8 s

    From the first equation of motion:

    v = u + at

    = 0 + 2.5 × 8

    = 20 m/s

    Therefore, after eight seconds, the velocity of the bus will be 20 m/s.

    The correct answer is C.

  • Question 2
    1 / -0

    Use the following information to answer the next question.

    A car is moving uniformly with a velocity of 28 km/h. It is accelerated at the rate of 2 m/s2 till it acquires a velocity of 54 km/h.

    What is the distance travelled by the car during its acceleration?

    Solution

    Initial velocity, u = 28 km/h =

    Final velocity, v = 54 km/h

    Acceleration, a = 2 m/s2

    Let the time taken be t.

    From the first equation of motion:

    v = u + at

    Now, using the second equation of motion:

    Therefore, the car travels a distance of 41.13 metres during its acceleration.

    The correct answer is D.

  • Question 3
    1 / -0

    A car starts from rest and accelerates uniformly at the rate of 3 m/s2. What is the distance travelled by the car in 12 seconds?

    Solution

    Initial velocity of the car, u = 0 (Since the car is initially at rest)

    Acceleration, a = 3 m/s2

    Time, t = 12 s

    Let the distance travelled by the car be s.

    Applying the second equation of motion:

    Therefore, the car travels a distance of 216 metres in 12 seconds.

    The correct answer is C.

  • Question 4
    1 / -0

    Use the following information to answer the next question.

    In the Beijing Olympic, sprinter Usain Bolt created a new world record by wining the 100 metres race in just 9.69 seconds.

    If his acceleration is considered to have been uniform throughout the race, then his velocity at the finishing line was

    Solution

    Initial velocity, u = 0

    Distance, s = 100 m

    Time, t = 9.69 s

    Using the position-time relation (The second equation of motion):

    Now, using the velocity-time relation (The first equation of motion):

    v = u + at

    = 0 + 2.13 × 9.69

    = 20.64 m/s

    Therefore, the velocity ofUsain Bolt at the finishing line was 20.64 m/s.

    The correct answer is C.

  • Question 5
    1 / -0

    Use the following information to answer the next question.

    A car starts from rest and acquires a uniform velocity of 72 km/h. During this while, it covers a distance of 120 metres.

    What is the acceleration produced in the car?

    Solution

    Initial velocity of the car, u = 0 (Since the car is initially at rest)

    Final velocity of the car, v = 72 km/h

    Distance travelled, s = 120 m

    Using the third equation of motion:

    v2 − u2 = 2as

    (20)2 = 2 × a × 120

    Therefore, the acceleration produced in the car is 1.67 m/s2.

    The correct answer is B.

  • Question 6
    1 / -0

    Use the following information to answer the next question.

    A geostationary satellite revolves around earth in a special orbit (known as the geosynchronous orbit) in such a way that it takes one day to complete one revolution around earth. This satellite revolves around earth with a speed of 3070 m/s.

    What is the approximate radius of the geosynchronous orbit?

    Solution

    Time of revolution, t = 1 day = 24 h = 86400 s

    Speed of the geostationary satellite, v = 3070 m/s

    Let the radius of the geosynchronous orbit be r.

    = 42236942.67 m

    = 42236.94 km

    ≈ 42237 km

    Therefore, the radius of thegeosynchronous orbit is approximately 42237 km.

    The correct answer is C.

  • Question 7
    1 / -0
    If Akshay is sitting on a Ferris wheel that is moving with a uniform speed of 1.5 m/s and the diameter of the wheel is 100 metres, after how much time will Akshay reach his initial position?

    Solution

    Diameter of the Ferris wheel, d = 100 m

    Radius of the Ferris wheel, r = m

    Speed of the wheel, v = 1.5 m/s

    Time taken by Akshay to reach his initial position = Time taken by the wheel to complete one revolution

    Speed of the Ferris wheel

    ⇒ Time taken =

    ≈ 3 min 30 s

    Therefore, Akshay will reach his initial position after approximately 3 minutes and 30 seconds.

    Hence, the correct answer is option B.

  • Question 8
    1 / -0

    Use the following information to answer the next question.

    The position-time graph of a moving particle is shown in the given figure.

    What is the average speed of the particle?

    Solution

    Average speed is given by the relation:

    Average speed

    Now, the total distance travelled by the particle is obtained from the graph as follows:

    Between 0 and 2 s, the particle covers a distance of 5 m

    Between 2 s and 4 s, the particle covers a distance of 15 m

    Between 4 s and 6 s, the particle covers a distance of 5 m

    Between 6 s and 8 s, the particle is at rest, i.e., the distance covered is 0

    Between 8 s and 10 s, the particle covers a distance of 10 m

    Between 10 s and 12 s, the particle covers a distance of 10 m

    ∴Total distance covered = 5 + 15 + 5 + 0 + 10 + 10 = 45 m

    Total time taken = 12 s

    ∴Average speed of the particle

    The correct answer is C.

  • Question 9
    1 / -0

    Use the following information to answer the next question.

    The velocities of a car at different intervals of time are shown in the given velocity-time graph.

    In which alternative is a line segment correctly matched with the nature of acceleration represented by that line segment in the graph?

    Solution

    In a velocity-time graph, a line parallel to the time axis represents no change in velocity. Since acceleration is defined as the rate of change of velocity with time, a line parallel to the time axis in a velocity-time graph represents zero acceleration. Hence, the line segment QR represents zero (or constant) acceleration of the car.

    The correct answer is C.

  • Question 10
    1 / -0

    Use the following information to answer the next question.

    Yana starts from her home and moves a distance of four kilometres toward East. She then turns to her right and covers a distance of three kilometres to reach her school. Meanwhile, her brother Nikhil takes a short and direct route to reach the school.

    What is the difference between the displacements of Yana and Nikhil?

    Solution

    Displacement is defined as the shortest distance between the initial and the final positions. The motion of Yana is shown in the following figure.

    Here, AB represents the distance travelled by Yana toward East, while BC is the distance travelled after she turns to her right.

    The initial (home) and final (school) positions are represented by A and C respectively.

    The shortest distance between her home and the school is:

    (AC)2 = (AB)2 + (BC)2

    = (4)2 + (3)2 = 25

    ∴AC = 5 km

    Hence, Yana’s displacement is 5 km.

    Her brother Nikhil takes the short and direct route. This means that Nikhil takes the path AC to reach C from A.

    Therefore, Nikhil’s displacement is also 5 km.

    Hence, the difference between the two displacements is 5 − 5 = 0 km.

    The correct answer is A.

  • Question 11
    1 / -0

    Yuvika runs around a square park of width 30 metres. What is the distance travelled by her after she completes five rounds of the park?

    Solution

    The path travelled by Yuvika is shown in the following figure.

    Distance travelled by Yuvika in one round = Perimeter of the square

    = 4 × (side) = 4 × 30 = 120 m

    Since she completes five rounds of the park, the total distance travelled by her = 5 × 120 = 600 m.

    The correct answer is D.

  • Question 12
    1 / -0

    Use the following information to answer the next question.

    A car is moving with a uniform velocity of 15 km/h. When the driver presses the accelerator, the velocity of the car increases uniformly to 45 km/h in five seconds.

    What are the respective values for the average velocity of the car and the acceleration produced in it during those five seconds?

    Solution

    Initial velocity of the car, u = 15 km/h

    Final velocity of the car, v = 45 km/h

    Time, t = 5 s

    Acceleration,

    Average velocity,

    The correct answer is A.

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