Answer:
a) 30 mph = 13 m/s. 65 mph = 29 m/s
b) The acceleration of the car is 2 m/s²
c) The car traveled 168 m in the 8 s interval.
Explanation:
Hi there!
a) Knowing that 1 mile = 1609.34 m and 1 h = 3600 s, let´s convert the velocities to m/s.
30 mi/ 1h · (1609.34 m/ 1 mi) · (1 h / 3600 s) = 13 m/s
65 mi/h · (1609.34 m/ 1 mi) · (1 h / 3600 s) = 29 m/s
b) The acceleration of the car can be obtained from the equation of velocity:
v = v0 + a · t
Where:
v = velocity of the car at time t
v0 = initial velocity
a = acceleration
t = time
Then, solving for acceleration:
(v - v0)/t = a
a = (29 m/s - 13 m/s) / 8 s = 2 m/s²
c) The position of the car can be calculated using the following equation:
x = x0 + v0 · t + 1/2 · a · t²
Where:
x = position of the car at time t
x0 = initial position
v0 = initial velocity
t = time
a = acceleration
If we place the origin of the frame of reference at the point where the car starts accelerating, then, x0 = 0.
x = 13 m/s · 8 s + 1/2 · 2m/s² · (8 s)²
x = 168 m
