Question

car accelerates from 10m/s to 25m/s in 6.0s what is its acceleration? how far did it travel in this time? assume constant acceleration

Answer 1

Acceleration = (change in speed) / (time for the change)

Change in speed = (end speed) minus (start speed)

Change in speed = (25 m/s) - (10 m/s) = 15 m/s .

Acceleration = (15 m/s) / (6 sec) =  2.5 m/s² .

Average speed during the acceleration = (1/2) (10 m/s + 25 m/s)

Average speed during the acceleration = (1/2) (35 m/s)

Average speed during the acceleration = 17.5 m/s

Traveling at the average speed of 17.5 m/s for 6 sec,  the car covers (17.5m/s x 6sec) = 105 meters.

The other way to solve it, using the formula:  D = v₀t + (1/2) a T²

Distance = (initial speed)(time) + (1/2)(acceleration)(time²)

Distance = (10 m/s)(6 sec) + (1/2)(2.5 m/s²)(6.0sec)²

Distance = (60 m) + (1/2)(2.5 m/s²)(36 sec²)

Distance = (60 m) + (45 m) = 105 meters