A car starts from rest and travels for 5.5 s
with a uniform deceleration of 1.3 m/s
2
.
What is the final velocity of the car?
Answer in units of m/s
Every second the speed changes by 1.3m/s. This continues for 5.5s
Hmmm. what to do. what to do.
How about 1.3 * 5.5 for the final velocity?
The only problem I see is that it started at rest, with v=0. Then the velocity decreases?
13.25
To find the final velocity of the car, we can use the formula for uniformly decelerated motion:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity (which is 0 m/s since the car starts from rest)
a = acceleration (deceleration in this case, which is -1.3 m/s^2)
s = displacement (unknown)
Since the car starts from rest, the initial velocity u is 0 m/s. Plugging in the values into the equation, we get:
v^2 = 0^2 + 2 * (-1.3 m/s^2) * s
Simplifying further:
v^2 = -2.6s
To find the final velocity v, we need the displacement s. However, we're only given the time (5.5 s) and the deceleration (-1.3 m/s^2), so we need to find the displacement first.
To find the displacement, we can use the equation for uniformly decelerated motion:
s = ut + (1/2)at^2
Where:
u = initial velocity (0 m/s)
a = acceleration (deceleration in this case, -1.3 m/s^2)
t = time taken (5.5 s)
Plugging in the values:
s = (0 m/s) * 5.5 s + (1/2) * (-1.3 m/s^2) * (5.5 s)^2
Simplifying further:
s = -4.6 m
Now that we have the displacement (s = -4.6 m), we can substitute it back into the equation to solve for the final velocity v:
v^2 = -2.6 * (-4.6 m)
v^2 = 11.96
Taking the square root of both sides to find v:
v ≈ 3.46 m/s
Therefore, the final velocity of the car is approximately 3.46 m/s.