a sports car can accelerate from 0 to 60 mph in 3.2s what is the acceleration of the car in m/s^2 what distance would it travel at this time
units conversion
a = v / t
d = Vave / t = 30 mph / 3.2 s
To find the acceleration of the car in m/s^2, we'll first need to convert the initial velocity (0 mph) and the final velocity (60 mph) to m/s.
1 mph ≈ 0.447 m/s
So, the final velocity (Vf) is 60 mph * 0.447 m/s = 26.82 m/s
Now, we can use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
a = (Vf - Vi) / t
Where:
Vf = final velocity = 26.82 m/s
Vi = initial velocity = 0 m/s
t = time taken = 3.2 s
Plugging in the values:
acceleration = (26.82 m/s - 0 m/s) / 3.2 s
acceleration = 26.82 m/s / 3.2 s
acceleration ≈ 8.38125 m/s^2 (rounded to 5 decimal places)
So, the acceleration of the car is approximately 8.38125 m/s^2.
Now, let's calculate the distance traveled at this time.
We can use the formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
where:
initial velocity (Vi) = 0 m/s
acceleration (a) = 8.38125 m/s^2
time (t) = 3.2 s
distance = (0 m/s * 3.2 s) + (0.5 * 8.38125 m/s^2 * (3.2 s)^2)
distance = 0 m + 0.5 * 8.38125 m/s^2 * 10.24 s^2
distance = 0 m + 41.90625 m
distance ≈ 41.91 m (rounded to 2 decimal places)
Therefore, the car would travel approximately 41.91 meters in this time.