Motion Test

Result

Motion Test - 43

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Weekly Quiz Competition

Question 1
1 / -0

A body initially at rest travels a distance 100 m in 5 s with a constant acceleration. Find the acceleration.

A
$$20 m s^{-2}$$

B
$$4 m s^{-2}$$

C
$$8 m s^{-2}$$

D
$$10 m s^{-2}$$

Solution

From equation of motion $$S = ut + \dfrac{1}{2}at^2$$
$$100=0 \times 5 + \dfrac{1}{2} \times a \times (5)^2$$
or $$ 100=\dfrac{1}{2} \times 25 a$$
or
Acceleration $$a=\dfrac{100 \times 2}{25}= 8 m s^{-2}$$
Question 2
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A body starts from rest with a uniform acceleration $$2 m s^{-2}$$. Find the distance covered by the body in $$2\ s$$.

A
$$4\ m$$

B
$$2 \ m$$

C
$$1 \ m$$

D
$$0 \ m$$

Solution

$$u = 0, a = 2 m/s^2, t = 2 s$$
Putting the values in $$S = ut+\dfrac{1}{2}at^2$$
$$S = 0\times 2+\dfrac{1}{2}\times 2\times 2^2$$
$$S = 4 m$$
Question 3
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Figure shows displacement-time graph of two vehicles A and B moving along a straight road. Which vehicle is moving faster?

A
Vehicle A

B
Vehicle B

C
Vehicle A = Vehicle B

D
None of the above

Solution

From the graph we observe that the slope of graph for A > slope of graph for B
Now slope of distance time curve is equal to velocity.
so,
velocity of A > velocity of B
Question 4
1 / -0

A bullet initially moving with a velocity $$20\ ms^{-1}$$ strikes a target and comes to rest after penetrating a distance 10 m in the target. Calculate the retardation caused by the target.

A
$$2 \, m \, s^{-2}$$

B
$$5 \, m \, s^{-2}$$

C
$$10\, m \, s^{-2}$$

D
$$20\, m \, s^{-2}$$

Solution

$$u=20 m/s, S=10 m, v=0$$
Putting these values in $$v^2 = u^2+2aS$$
$$0 = 20^2+2a \times 10$$
$$a = -20 m/s^2$$
Hence, $$\text{Retardation} = 20 m/s^2$$
Question 5
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A body starts with an initial velocity of $$10 m s^{-1}$$ and acceleration $$5 m s^{-2}$$. Find the distance covered by it in $$5\ s$$.

A
$$62.5\ m$$

B
$$32.5\ m$$

C
$$112.5\ m$$

D
$$50\ m$$

Solution

$$u=10 m/s, a=5 m/s^2, t=5 s$$
$$S = ut+\dfrac{1}{2}at^2$$
$$S = 10\times 5+\dfrac{1}{2}\times 5\times 5^2$$
$$S = 112.5 m$$
Question 6
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A train moving with a velocity of $$20\ ms^{-1}$$ is brought to rest by applying the brakes in 5 s. Calculate the retardation.

A
$$4 m s^{-2}$$

B
$$2 m s^{-2}$$

C
$$1 m s^{-2}$$

D
$$8 m s^{-2}$$

Solution

$$u = 20 m/s, v=0, t=5 s$$
$$v=u+at$$
$$0=20+a\times 5$$
$$a = -4 m/s^2$$
Therefore, $$\text{Retardation} =4 m/s^2$$
Question 7
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A toy car, initially moving with a uniform velocity of $$18 \ km h^{-1}$$ comes to rest in $$2\ s$$. Find the retardation of the car in S.I units.

A
$$9 m s^{-2}$$

B
$$25 m s^{-2}$$

C
$$2.5 m s^{-2}$$

D
$$5 m s^{-2}$$

Solution

Velocity, $$v = \dfrac{18\times1000 m}{60\times60 s} = 5 m/s $$

Using formula $$v=u-at$$, where $$v=0$$ and $$u=5 m/s$$
Therefore, retardation, $$a = \dfrac{u}{t} = \dfrac{5 m/s}{2 s} = 2.5 m/s^2 $$
Question 8
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The expression for the displacement $$s$$ covered in time $$t$$ by a body which is initially at rest and starts moving with a constant acceleration $$a$$ is:

A
$$s=\dfrac{1}{2} at $$

B
$$s=\dfrac{1}{2} at ^2$$

C
$$s= at ^2$$

D
$$s=\dfrac{1}{2} ua ^2$$

Solution

For a body which is initially at rest, $$u = 0$$
Putting the value of $$u$$ in the second equation of motion,
$$s = ut+\dfrac{1}{2}at^2$$
$$s = \dfrac{1}{2}at^2$$
Question 9
1 / -0

A body initially at rest starts moving with a constant acceleration $$2\ ms^{-2}$$. Calculate the distance traveled in 5 s.

A
50 m

B
12.5 m

C
25 m

D
5 m

Solution

$$S=ut+\dfrac{1}{2}at^2$$
$$S = 0\times 5+\dfrac{1}{2}\times 2\times 5^2 = 25 m$$
Question 10
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Which of the following displacement-time graphs represents a uniform motion ?

A

B

C

D

Solution

In uniform motion, object covers equal distances in equal intervals of time, however small these time intervals may be in the same fixed direction.