A car accelerates uniformly from rest to a speed of 23.7 km/h in 6.5 s. Find the distance the car travels during this time.
The correct answer and explanation is :
To find the distance the car travels during this time, we can use the equations of uniformly accelerated motion. Specifically, we can use the formula:
[
d = v_i t + \frac{1}{2} a t^2
]
Where:
- (d) is the distance traveled,
- (v_i) is the initial velocity,
- (a) is the acceleration,
- (t) is the time.
Step 1: Analyze the given information
- The car accelerates from rest, so the initial velocity (v_i = 0 \, \text{m/s}).
- The final velocity is given as 23.7 km/h. To use consistent units (meters per second), we need to convert the speed into m/s:
[
23.7 \, \text{km/h} = 23.7 \times \frac{1000}{3600} \, \text{m/s} = 6.583 \, \text{m/s}
]
- The time is given as 6.5 seconds.
Step 2: Calculate the acceleration
Since the car starts from rest, the acceleration can be found using the formula for uniform acceleration:
[
v_f = v_i + a t
]
Where:
- (v_f) is the final velocity,
- (v_i) is the initial velocity (0 m/s),
- (a) is the acceleration,
- (t