Question

An automobile traveling along a straight road
increases its speed from 53 ft/s to 68 ft/s in
180 ft.
If the acceleration is constant. how much
time elapses while the auto moves the 180 ft?
Answer in units of s.

Answer 1

Answer:

t = 2.97[s]

Explanation:

To solve this problem we must use the following kinematics equations, we must bear in mind that the positive sign of the acceleration value means that the car is increased its speed.

$v_{f}^{2} =v_{o}^{2} +(2*a*(x-x_{o} ))$

where:

x - xo = 180 [ft]

a = acceleration [ft/s^2]

Vo = initial velocity = 53 [ft/s]

Vf = final velocity = 68 [ft/s]

Now replacing we find:

(68^2) = (53^2) + (2*a*180)

a = 5.04 [ft/s^2]

Now using the following equation:

$v_{f}=v_{0}+a*t$

68 = 53 + (5.04*t)

t = (68 - 53)/5.04

t = 2.97[s]