A certain car is capable of accelerating at a rate of +0.60 m/s2. How long does it take for this car to go from a speed of 20 mi/h to a speed of 65 mi/h?
acceleration = change of speed / time
but make sure the units are consistent.
change of speed
= (65-20) mph
=x m/s (find x)
0.60 = x/t
or
t=x/0.6 seconds
To determine how long it takes for the car to go from a speed of 20 mi/h to 65 mi/h, we first need to convert these speeds to meters per second (m/s) as the acceleration is given in m/s^2.
1 mile = 1609.34 meters
1 hour = 3600 seconds
Converting 20 mi/h to m/s:
20 mi/h * (1609.34 m/1 mi) / (3600 s/1 h) ≈ 8.94 m/s
Converting 65 mi/h to m/s:
65 mi/h * (1609.34 m/1 mi) / (3600 s/1 h) ≈ 29.06 m/s
Now that we have the initial and final speeds in m/s, we can calculate the time it takes using the formula:
t = (v_f - v_i) / a
where:
- t is the time (in seconds)
- v_f is the final velocity (29.06 m/s)
- v_i is the initial velocity (8.94 m/s)
- a is the acceleration (+0.60 m/s^2)
Plugging in the values:
t = (29.06 m/s - 8.94 m/s) / (0.60 m/s^2)
t ≈ 33.20 seconds
Therefore, it will take approximately 33.20 seconds for the car to go from a speed of 20 mi/h to a speed of 65 mi/h.