Final answer:
The acceleration of a car that goes from rest to a speed of 77 km/h in 8 seconds is 2.67 m/s² after converting the speed into meters per second and using the formula for uniform acceleration.
Step-by-step explanation:
To find the acceleration of a car that uniformly accelerates from rest to a speed of 77 km/h in 8 seconds, we first convert the speed to meters per second (m/s) because the standard unit of acceleration is meters per second squared (m/s2). Since 1 km/h is equal to 0.27778 m/s, 77 km/h is equivalent to 77 × 0.27778 m/s, which is approximately 21.3886 m/s.
The formula for uniform acceleration (a) is:
a = Δv / t
where,
- Δv is the change in velocity (final velocity - initial velocity)
- t is the time taken
Since the car starts from rest, the initial velocity (vi) is 0 m/s.
Thus,
a = (21.3886 m/s - 0 m/s) / 8 s = 2.673575 m/s2
Therefore, the car's acceleration is 2.67 m/s2.