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An automobile traveling 35 mi/h (= 56 km/h) is 110 ft (= 34 m) from a barrier when the driver slams on the brakes. Four seconds later the car hits the barrier. (a) What was the auto- mobile's constant deceleration before impact? (b) How fast was the car traveling at impact?

An automobile traveling 35 mi/h (= 56 km/h) is 110 ft (= 34 m) from a barrier when the driver slams on the brakes. Four seconds later the car hits the barrier. (a) What was the auto- mobile's constant deceleration before impact? (b) How fast was the car traveling at impact?

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
Given:
Initial speed of the car,. v0 = 56 km/h.
Distance of car from the barrier, x = 100 ft x.
Time taken by the car to hit the barrier, t = 4.0 s.
(a)Let us assume that the acceleration of the car is given by a. Then from the equation of kinematics, we have
232-1156_12.PNG
Rounding off to two significant figures
a = -12 ft/s2

The negative sign in the acceleration indicates that it acts in the direction opposite to that to the direction of initial velocity.
Therefore the deceleration of the car is -12 ft/s2
(b) Given:
Initial speed of car in ft / s (calculated above), v0 = 51 ft/s.
Let us assume that the final speed of the car, when it hit the barrier is given by v. Therefore one can calculate the final speed using the definition of the acceleration as:
232-1119_15.PNG

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