Motion in A Straight Line Test

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Motion in A Straight Line Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

When a ball is thrown vertically upwards, it reaches a maximum height of 5m. The initial velocity of the ball was ?

A
5 m/s

B
50 m/s

C
10 m/s

D
25 m/s

Solution

Answer is C.

The equation is given as $${ v }^{ 2 }-{ u }^{ 2 }=2as$$.
where,
v = final velocity,
u = initial velocity,
a = acceleration due to gravity, $$10\quad m/{ s }^{ 2 }$$,
s = h = height traveled.
Therefore, we can find u with above info. In this case, v = 0 at the top of the path.
$$0-{ u }^{ 2 }=2\times 10\times 5\quad =\quad 10\quad m/s.$$
Hence, the initial velocity of the ball was 10 m/s.
Question 2
1 / -0

A body will have uniform acceleration if its

A
speed changes at uniform rate

B
velocity changes at uniform rate

C
speed changes at non-uniform rate

D
velocity remains constant

Solution

If the velocity of an object changes at a uniform rate, then the acceleration that causes the change in velocity is called uniform acceleration or constant acceleration.
For example, the force of gravity imparts an acceleration uniformly which is called acceleration due to gravity.
Hence,option B is correct.
Question 3
1 / -0

The body will speed up if ___________ .

A
Velocity and acceleration are in same direction

B
Velocity and acceleration are in opposite direction

C
Velocity and acceleration are in perpendicular direction

D
None of these

Solution

A body will speed up if both velocity and acceleration are in same direction. If they are in opposite directions it results in slowing down the motion. And if they are perpendicular then there will be no effect on magnitude of velocity.
Question 4
1 / -0

A stone falls from a balloon that is descending at a uniform rate of $$12ms^{-1}$$. The displacement of the stone from the point of release after 10sec is :-

A
490m

B
510m

C
610m

D
725m

Solution

$$S=12\times 10+\dfrac { 1 }{ 2 } \times 9.8\times { 10 }^{ 2 }\\ \ \ =120+490\\ \ \ =610\ m$$
Question 5
1 / -0

Which of the following is/are equations of uniformly accelerated motion relating the initial velocity (u), final velocity (v), time (t), acceleration (a) and displacement (S).

A
$${v^2 = u^2+2aS} $$

B
$$ {v = u+at} $$

C
$$ {S = ut+\dfrac{1}{2}at^2} $$

D
All the above
Solution
The equations of motion relate to the following five quantities:
u - initial velocity
v - final velocity
a - acceleration
t - time
s - displacement
Of the above u, v, a, and s are vector quantities. As such, remember to make vectors going in one direction positive and vectors in the opposite direction negative.
Time (t) is a scalar quantity.
If any three of the five quantities are known then the other two may be calculated using the following three equations:
- $$v=u+at$$
- $$s=ut+\frac { 1 }{ 2 } at^{ 2 }$$
- $${ v }^{ 2 }{ =u }^{ 2 }+2as$$
The equations of motion can only be used for an object travelling in a straight line with a constant acceleration.
Question 6
1 / -0

When an object is accelerated:

A
its direction must be constant

B
its velocity is necessarily changing

C
its velocity is constant

D
its speed is necessarily changing

Solution

Acceleration is the time rate of change of velocity.
Question 7
1 / -0

Directions For Questions

A car is moving on a straight road with constant acceleration. The initial velocity of the car is 5 m/s and after 10 seconds its velocity becomes 25 m/s.

...view full instructions

(a) Find the acceleration of the car

A
$$\, 2\, m/s^2$$

B
$$4 m/s^2$$

C
$$6 m/s^2$$

D
$$8 m/s^2$$

Solution

Given:
Initial velocity $$u=5\ m/s$$
Final velocity $$v=25\ m/s$$
Time $$t=10\ s$$
From the equation of motion $$v=u+at$$ we get,
acceleration $$a=\dfrac{v-u}{t}=\dfrac{25-5}{10}=2\ m/s^2$$
Question 8
1 / -0

A particle experiences constant acceleration for $$20 s$$ after starting from rest. If it travels a distance $${X}_{1}$$, in the first $$10 s$$ and distance $${X}_{2}$$, in the remaining $$10 s$$, then which of the following is true ?

A
$${X}_{1} = 2{X}_{2}$$

B
$${X}_{1} = {X}_{2}$$

C
$${X}_{1} = 3{X}_{2}$$

D
None of these

Solution

from eq $$s=ut+(1/2)a(t^2)$$

initial velocity $$u=0 m/sec$$ (particle starts from rest)

$$x_1=(1/2)a(t^2)$$

$$x_1=(1/2)a(10^2)$$

$$x_1=50a$$ ------------------(1)

now initial velocity for $$x_2$$ is the final velocity of $$x_1$$

let final velocity of $$x_1$$=initial velocity of $$x_2=v$$

so, $$v=u +at$$

$$v=at$$

$$ v=10a$$ (since u=0 and t=10)

now $$x_2=ut+(1/2)a(t^2)$$

$$x_2=(10a)*10+(1/2)a(10^2)$$

$$x_2=100a+50a$$

$$x_2=150a$$ -------------------------(2)

now

$$\dfrac{(2)}{(1)}=\dfrac{x_1}{x_2}$$

$$\dfrac{x_1}{x_2}=\dfrac{50a}{150a}$$

$$3x_1=x_2$$
Question 9
1 / -0

Velocity-time graph of a body with uniform velocity is a straight line

A
Parallel to x-axis

B
Parallel to y-axis

C
Inclined to x-axis

D
Inclined to y-axis

Solution

Velocity-time graph of an object moving with uniform velocity. The slope of a Velocity–time graph of an object moving in rectilinear motion with uniform velocity is straight line and parallel to x-axis when velocity is taken along y-axis and time is taken along x-axis.
Question 10
1 / -0

Area under a speed-time graph gives :

A
The time taken by a moving object

B
The distance travelled by a moving object

C
Tthe acceleration of a moving object

D
Tthe retardation of a moving object

Solution

The area under the velocity-time graph gives the distance traveled by a moving object during that time interval.
While the area under the velocity-time graph gives displacement of the particle.

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Motion in A Straight Line Test - 15

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Motion in A Straight Line Test - 15

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Question 1

5 m/s

50 m/s

10 m/s

25 m/s

Solution

Question 2

speed changes at uniform rate

velocity changes at uniform rate

speed changes at non-uniform rate

velocity remains constant

Solution

Question 3

Velocity and acceleration are in same direction

Velocity and acceleration are in opposite direction

Velocity and acceleration are in perpendicular direction

None of these

Solution

Question 4

490m

510m

610m

725m

Solution

Question 5

$${v^2 = u^2+2aS} $$

$$ {v = u+at} $$

$$ {S = ut+\dfrac{1}{2}at^2} $$

All the above

Solution

Question 6

its direction must be constant

its velocity is necessarily changing

its velocity is constant

its speed is necessarily changing

Solution

Question 7

$$\, 2\, m/s^2$$

$$4 m/s^2$$

$$6 m/s^2$$

$$8 m/s^2$$

Solution

Question 8

$${X}_{1} = 2{X}_{2}$$

$${X}_{1} = {X}_{2}$$

$${X}_{1} = 3{X}_{2}$$

None of these

Solution

Question 9

Parallel to x-axis

Parallel to y-axis

Inclined to x-axis

Inclined to y-axis

Solution

Question 10

The time taken by a moving object

The distance travelled by a moving object

Tthe acceleration of a moving object

Tthe retardation of a moving object

Solution

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