Question

A car is traveling with an initial velocity of 15 m/s when the driver decides to go faster by accelerating at 5 m/s squared for 10 seconds. How far did the car travel during this time?

Answer 1

Answer:

x = 400 [m]

Explanation:

To solve this problem we must use the following kinematics equations, first, we find the final speed, and then we proceed to find the distance traveled.

$v_{f}=v_{i} +(a*t)$

where:

Vf = final velocity [m/s]

Vi = initial velocity = 15 [m/s]

a = acceleration = 5 [m/s^2]

t = time = 10 [s]

Note: the positive sign in the Equation indicates that the car is accelerating, i.e. its speed is increasing.

Now replacing

Vf = 15 + (5*10)

Vf = 65 [m/s]

Now using the second equation:

$v_{f} ^{2}= v_{i} ^{2}+(2*a*x)$

where:

x = distance traveled [m]

x = (65^2 - 15^2)/ (2*5)

x = 400 [m]