Question

A racing car reaches a speed of 40 m/s. At this instant, it begins a uniform negative acceleration, using a parachute and a braking system, and comes to rest 5.0 s later. (a) Determine the acceleration of the car. (b) How far does the car travel after the acceleration starts?

Answer 1

Step-by-step explanation:

v=u+at

v= final velocity

u= initial velocity

a=acceleration

t= time

the final velocity=0 as it became to rest

v=u+at

0= 40 +(-a)*5

-40=-a*5

a=8

∴ the negative acceleration (deceleration) of the car is 8ms^-2

s=ut + 1/2at^2

s= 40*5 - 1/2*8*25

s= 200- 100

s=100m

Therefore, the car travels 100m after the acceleration.

Answer 2

a) - 8 m/s₂

b) 100 meters

Step-by-step explanation:

The equation relating final velocity, initial velocity, acceleration and time to reach final velocity from initial velocity is given by

v = u + at

where
v = final velocity
u = initial velocity
a = acceleration
t = time taken

Here the dragster starts at 40m/s and comes to a total stop after 5 seconds

Therefore v = 0, u = 40 m/s and t = 5 seconds

Plugging this in:
0 = 40 - a · 5

0 = 40 + 5a

5a = - 40

a = -40/5 = -8 m/s²

The negative sign indicates it is deceleration rather than acceleration

The distance traveled is given by the formula
d = vₐ x t
where
d = distance traveled
vₐ = average velocity
t = time taken

Since acceleration(or, in this case deceleration) is uniform
average velocity

vₐ = 1/2 x (u + v) = 1/2 x (0 + 40) = 20 m/s

d = 20 x 5 = 100 meters