While approaching a red light, a student driver begins to
apply the brakes. If the car’s brakes can cause an average
acceleration of 2.90 m/s2 [S] and it takes 5.72 s for the
car to come to rest, what was the car’s initial velocity?
v = Vi + a t
0 = Vi - 2.90 m/s^2 * t
Vi = 2.90 m/s^2 * 5.72 s
= 16.59 m/s
Well, let's use our amazing clown maths skills to solve this problem! If the car's brakes can cause an average acceleration of 2.90 m/s² [S] and it takes 5.72 s for the car to come to rest, we can use the equation:
vf = vi + at
Where vf is the final velocity (which is 0 because the car comes to rest), vi is the initial velocity, a is the acceleration, and t is the time.
Plugging in the values we know: vf = 0 m/s, a = -2.90 m/s² (negative because the car is decelerating), and t = 5.72 s, we can rearrange the equation to solve for vi:
0 = vi + (-2.90 m/s²)(5.72 s)
Now, let's get our clown calculator out...
0 = vi - 16.588 m/s
Adding 16.588 m/s to both sides, we find:
vi = 16.588 m/s
So, the car's initial velocity was approximately 16.588 m/s. Hopefully, the student driver wasn't in a hurry to go somewhere too exciting!
To find the car's initial velocity, we can use the kinematic equation:
v = u + at
where:
v = final velocity (0 m/s, as the car comes to rest)
u = initial velocity (what we want to find)
a = average acceleration (-2.90 m/s^2, as the acceleration is in the opposite direction)
t = time taken (5.72 s)
Rearranging the equation, we have:
u = v - at
Substituting the given values:
u = 0 - (-2.90 m/s^2 × 5.72 s)
u = 0 + 16.628 m/s
u ≈ 16.63 m/s
Therefore, the car's initial velocity was approximately 16.63 m/s.
To find the initial velocity of the car, we can use the formula:
v = u + at
Where:
v = final velocity (in this case, the car comes to rest, so v = 0 m/s)
u = initial velocity
a = acceleration
t = time
Rearranging the formula, we get:
u = (v - at)
Now we can substitute the given values into the formula:
v = 0 m/s (car comes to rest)
a = 2.90 m/s^2
t = 5.72 s
Plugging in the values, we get:
u = (0 - 2.90 * 5.72)
Simplifying the equation:
u = -16.588
Now, it's important to note that the negative sign in this context indicates that the car was moving in the opposite direction of the positive direction we assumed. So we ignore the negative sign and take the magnitude of the initial velocity. Therefore, the car's initial velocity is approximately 16.588 m/s.