Calculating Final Speed of a Car with Acceleration - Homework Solution

[cbrowne]

Could some one please confirm my answer. Thanks

Homework Statement

A car was moving on the highway at a speed of 90 km/h. The driver then stepped
on the gas and started to accelerate uniformly at a rate of 0.26 m/s^2, and he was
able to overtake a truck in 35 s.

What was the final speed of the car after this
time?

Homework Equations

The Attempt at a Solution

90km = 25 m/s

0.26m/s^2 x 35sec = 9.1 m/s

Therefore, the car was originally traveling @ 25m/s and with acceleration it gained 9.1 m/s.


25 m/s + 9.1 m/s = 34.1 m/s--- converted to 123 km/h

 

[unscientific]

yes its correct. Leave your answer in m/s please. Its the S.I. unit for length and time.

 

[thomate1]

as the final speed of the car.

Your solution is correct. To confirm, we can use the formula for final speed (vf) with initial speed (vi), acceleration (a), and time (t):

vf = vi + at

Plugging in the values:

vf = 25 m/s + (0.26 m/s^2)(35 s)

vf = 25 m/s + 9.1 m/s

vf = 34.1 m/s

Converting to km/h:

vf = 34.1 m/s x (3.6 km/h / 1 m/s)

vf = 123 km/h

Therefore, the final speed of the car after 35 seconds of acceleration is indeed 123 km/h. Great job!