Question

A ball rolls onto the path of your car as you drive down a quiet neighborhood street. To avoid hitting the child that runs to retrieve the ball, you apply your brakes for 1.30 s. The car slows down from 15.0 m/s to 9.00 m/s. The mass of the car is 1040 kg.
(a) During the time the brakes were applied, what was the average force exerted on your car?
(b) Was the average force exerted on your car forwards or backwards?
(c) How far did the car move while braking?

Answer 1

Answer:

a) F = -1035.385 N

b) Backwards

c) s = 15.60 m

Explanation:

Given information

$u$ = Initial Speed of Car = 15.0 m/s

$v$ = Final Speed of Car = 9.00 m/s

$t_{b}$ = Breaking Time = 1.30 s

$m$ = Mass of Car = 1040 kg

Part (a)

To find the force exerted on the car we use the following formula

$F = ma$

Where

$F$ = Force = unknown

$m$ = Mass of Car = 1040 kg

$a$ = Acceleration of Car / Deceleration of Car = unknown

To find the force (F) we need to first find the deceleration rate (a)

To find the deceleration rate we use the following formula

$a = \frac{v - u}{t}$

Inputting the given values

$a = \frac{15 - 9}{1.30} \\ a = -4.615$

To find the force

$F = ma \\ F = (1040)(-4.615) \\ F = (1040)(-4.615) \\ F = -1035.385 N$

Part (b)

Since the value of F is negative this means the the force was opposite the direction of motion, hence the force was backwards.

Part (c)

To find the total distance the car moved while braking we use the following formula

$v^2 = u^2 + 2as$

Where

$s$ = distance traveled

Inputting the values given

$(9)^2 = (15)^2 + 2(-4.615)s$

$s = 15.60 m$