Question

A commuter backs her car out of her garage with an acceleration of 1.50 m/s² .

(a) How long does it take her to reach a speed of 1.60 m/s?
(b) If she then brakes to a stop in 0.8 s, what is her decelerationin m/s²?

Answer 1

The car takes 1.43 seconds to reach a speed of 2.00 m/s and has a deceleration of -2.50 m/s².

Step-by-step explanation:

(a) To find the time it takes for the car to reach a speed of 2.00 m/s, we can use the formula:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Plugging in the given values:

u = 0 (assuming the car starts from rest)
a = 1.40 m/s²
v = 2.00 m/s

we can rearrange the formula to solve for t:

t = (v - u) / a

Substituting the values, we have:

t = (2.00 - 0) / 1.40 = 1.43 seconds

(b) To find the deceleration, we can use the formula:

a = (v - u) / t

where a is the acceleration (deceleration in this case), v is the final velocity (0 m/s in this case, since the car comes to a stop), u is the initial velocity (2.00 m/s), and t is the time (0.800 s).

Plugging in the given values:

a = (0 - 2.00) / 0.800 = -2.50 m/s²