A motorcyclist sees a branch in the road, and slows down at -6.42 m/s?. If it takes them 2.85s to stop, what was their starting velocity?
To find the starting velocity of the motorcyclist, we can use the formula:
V = V0 + at,
Where:
V0 = initial velocity,
V = final velocity,
a = acceleration, and
t = time.
In this case, the final velocity (V) is 0 m/s since the motorcyclist stops. The acceleration (a) is -6.42 m/s² since the motorcyclist slows down at this rate. The time (t) is given as 2.85 s.
Plugging these values into the formula, we have:
0 = V0 + (-6.42)(2.85),
Simplifying the equation:
0 = V0 - 18.327.
Solving for V0, we see that:
V0 = 18.327 m/s.
Hence, the starting velocity of the motorcyclist was 18.327 m/s.
To find the starting velocity of the motorcyclist, we need to use the equation of motion that relates velocity, acceleration, and time:
vf = vi + at
Where:
vf = final velocity (which is 0 since the motorcyclist comes to a stop)
vi = initial velocity (what we need to find)
a = acceleration (in this case, the deceleration due to braking, which is unknown)
t = time (given as 2.85s)
Rearranging the equation, we have:
vi = vf - at
Substituting the values we have:
vf = 0 m/s (since the motorcyclist comes to a stop)
a = -6.42 m/s² (negative because the motorcyclist is decelerating)
t = 2.85 s
Plugging in the values, we can find the initial velocity:
vi = 0 - (-6.42 * 2.85)
Simplifying the equation:
vi = 0 + 18.327
Calculating further:
vi = 18.327 m/s
Therefore, the motorcyclist's starting velocity was 18.327 m/s.
To find the motorcyclist's starting velocity, we can use the equation of motion:
v = u + at
where:
v = final velocity (0 m/s as the motorcycle comes to a stop)
u = initial velocity (what we want to find)
a = acceleration (assumed to be constant)
t = time taken to stop (2.85 s)
In this case, the acceleration is given by the change in velocity divided by the time taken to stop:
a = (final velocity - initial velocity) / t
Substituting the given values:
0 m/s = u + a * 2.85 s
We also know that the motorcyclist slowed down by 6.42 m/s during this time, so:
0 m/s = u + (-6.42 m/s) * 2.85 s
Now, we can solve for u:
0 m/s = u - 18.327 m/s
To isolate u, we rearrange the equation:
u = 18.327 m/s
Therefore, the motorcyclist's initial velocity was 18.327 m/s.