A driver of a car traveling at 14.5 m/s applies
the brakes, causing a uniform deceleration of
1.7 m/s
2
.
How long does it take the car to accelerate
to a final speed of 9.50 m/s?
Answer in units of s
To find the time it takes for the car to accelerate to a final speed of 9.50 m/s, we can use one of the equations of motion known as the first equation of motion:
v = u + at
where:
v = final velocity (9.50 m/s)
u = initial velocity (14.5 m/s)
a = acceleration (deceleration in this case, which is -1.7 m/s^2)
t = time
First, let's rearrange the equation to solve for time (t):
t = (v - u) / a
Now, substitute the values into the equation:
t = (9.50 m/s - 14.5 m/s) / (-1.7 m/s^2)
Now, calculate the time:
t = (-5.00 m/s) / (-1.7 m/s^2)
= 2.94 s (rounded to two decimal places)
Therefore, it takes approximately 2.94 seconds for the car to accelerate to a final speed of 9.50 m/s.