A motorist travelling at 20 m/s, sees a child on the road,
when he is 150 m away from the child. He immediately
applies the brakes and the car decelerates uniformly at
the rate of 2 m/s?. His reaction time is 0.5 second. What
is the distance between the car and the child, when the car
comes to rest
(a) 20 m
(b) 30 m
(c) 40 m
(d) 50 m
Answers
Oᴘᴛɪᴏɴ D
50ᴍ
Hᴏᴘᴇ ᴜ ᴜɴᴅᴇʀsᴛᴀɴᴅ
Tᴀɢ ᴍᴇ ᴀs ʙʀᴀɪɴʟɪᴇsᴛ
The answer is (c) 40m.
Given: Initial velocity of the motorist(u) = 20m/s
Distance between the motorist and the child = 150m
Reaction time(t₁) = 0.5 seconds
Rate of deceleration of the car (a) = 2m/s²
To Find: Distance between the car and the child when it comes to rest
Solution:
Reaction time is the time taken by a person to react to a situation. Till the reaction time, there will be no deceleration and the motorist will travel at the same velocity as before.
Speed = Distance / Time
20 = Distance / 0.5
Distance(s₁) = 20 x 0.5
= 10 m
When the car comes to rest, the final velocity of the car will be zero
Final velocity(v) = 0
Let us consider the direction of motion of the car as positive, so the deceleration will be negative a = - 2m/s²
Using the equation of motion,
v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration and s is the distance covered.
0² = (20)² + 2(-2)(s₂)
4(s₂) = 400
s₂ = 100 m
The total distance covered by the car before stopping = s₁ + s₂
= 10 + 100
The total distance covered by the car before stopping = 110m
The separation between the child and the car after stopping = Initial separation between the child and the car - Distance covered by the car before stopping
The separation between the child and the car after stopping = 150 - 110
= 40m
Therefore, the separation between the car and the child after the car has stopped is 40m.