Final answer:
To calculate the time taken for a car to accelerate from 30 mi/h to 40 mi/h with an acceleration of 0.62 m/s², convert the speeds to meters per second and use the kinematic equation. After conversion and calculation, it takes approximately 7.21 seconds for the acceleration.
Step-by-step explanation:
To find out how long it takes for a car to go from a speed of 30 mi/h to a speed of 40 mi/h with an acceleration of 0.62 m/s2, you need to perform the following calculations:
First, convert the speeds from miles per hour to meters per second:
- 30 mi/h is approximately 13.41 m/s (1 mi/h is approximately 0.44704 m/s).
- 40 mi/h is approximately 17.88 m/s.
Now use the kinematic equation which relates final speed (vf), initial speed (vi), acceleration (a), and time (t):
vf = vi + a×t
Plug in the values:
17.88 m/s = 13.41 m/s + (0.62 m/s2)×t
Solving for t gives:
t = (17.88 m/s - 13.41 m/s) / 0.62 m/s2
t = 7.21 s
So, it takes approximately 7.21 seconds for the car to accelerate from 30 mi/h to 40 mi/h.