Q.

A car moves with a constant velocity of 10 ms–1 for 10 s along a straight track, then it moves with uniform acceleration of 2 ms–2 for 5 seconds. Find the total displacement and velocity at the end of the 5th second of acceleration.

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a

20 m/s, 145 m

b

20 m/s, 175 m

c

10 m/s, 165 m

d

25 m/s, 185 m

answer is C.

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Detailed Solution

Let v1 and t1 be the initial velocity and the time for the first part where the car is moving with a constant velocity.

t1 = 10 s; v1 = 10 m s–1

Distance travelled s1 = v1 t1

i.e., s1 = 10 × 10 = 100 m

For the second part, i.e., when the car accelerates,

a = 2 m s–2, v =?

t = 5 seconds s2 =?

u = 10 m s–1

v = u + at

v = 10 + 2 × 5

v = 10 + 10

Þ v = 20 ms–1

s2=ut+12at2 s2=10×5+12×2×52 =50+1×25=50+25=75 m  Total displacement s=s1+s2 s=100+75=175 m.

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