A car decelerates uniformly and comes to a stop after 9 seconds. The car's average velocity during deceleration was 45 km/h. What was the cars deceleration while slowing down?
To determine the car's deceleration while slowing down, we can use the formula for constant acceleration:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, the car comes to a stop, so the final velocity (v) is 0 km/h. The initial velocity (u) is given as 45 km/h. The time (t) is given as 9 seconds.
Using the formula, we can solve for the acceleration (a):
0 = 45 km/h + a * 9 seconds
First, let's convert the initial velocity from km/h to m/s, since the units of time are in seconds:
45 km/h = (45 * 1000) / (60 * 60) m/s = 12.5 m/s
Now, let's rearrange the equation to solve for acceleration (a):
a * 9 seconds = -12.5 m/s
Dividing both sides by 9 seconds:
a = -12.5 m/s / 9 seconds
Therefore, the car's deceleration while slowing down is approximately -1.39 m/s². The negative sign indicates that the car is decelerating, or slowing down. Note that negative acceleration is also referred to as deceleration.
To find the car's deceleration while slowing down, we can use the formula:
deceleration = (final velocity - initial velocity) / time
Given:
initial velocity = 45 km/h
final velocity = 0 km/h
time = 9 seconds
Converting the velocities to m/s:
initial velocity = 45 km/h = 45 * (1000/3600) m/s ≈ 12.5 m/s
final velocity = 0 km/h = 0 m/s
Plugging the values into the formula:
deceleration = (0 - 12.5) m/s / 9 s
= -12.5 m/s / 9 s (negative because the car is decelerating)
Simplifying:
deceleration ≈ -1.39 m/s²
Therefore, the car's deceleration while slowing down is approximately -1.39 m/s².