A car starts from rest and accelerates uniformly over a time of 6.5 seconds for a distance of 150 m. Determine the acceleration of the car.
Average speed Vav = 150/6.5 = 23.1 m/s
Final speed Vf = 2*Vav = 46.2 m/s
Acceleration = Vf/(time) = 46.2/6.5 = ___ m/s^2
7.107m/s^2
To determine the acceleration of the car, we can use the formula:
acceleration = (final velocity - initial velocity) / time
We know that the car starts from rest, which means the initial velocity, u, is 0 m/s.
The final velocity, v, can be calculated using the formula:
v = u + (acceleration * time)
Since the car starts from rest, the final velocity will be equal to the average velocity, which can be calculated using the formula:
average velocity = (initial velocity + final velocity) / 2
In this case, the average velocity will be (0 + v) / 2 = v / 2.
We can substitute this into the formula for distance:
distance = average velocity * time
Substituting the value of average velocity, we get:
distance = (v / 2) * time
Rearranging the equation to solve for v, we have:
v = (2 * distance) / time
Now we can substitute this value of v in the equation for acceleration:
acceleration = (v - u) / time
acceleration = ([(2 * distance) / time] - 0) / time
acceleration = (2 * distance) / (time * time)
Plugging in the given values:
acceleration = (2 * 150 m) / (6.5 s * 6.5 s)
Calculating this, we find:
acceleration = 4.62 m/s²
Therefore, the acceleration of the car is 4.62 m/s².