How does one go about solving this?
A skateboard rider starts from rest and accelerates at a constant +.50 m/s^2 for 8.4s. What is the riders displacement?
X = (1/2) a t^2
a is the acceleration
t is the time
X is the displacement
The formula applies when the initial velocity is zero, as in this case.
thanks! I forgot the formula >.<
To solve for the rider's displacement, you can use the following equation of motion:
displacement = initial velocity * time + (1/2) * acceleration * time^2
In this case:
- The rider starts from rest, which means the initial velocity is 0 m/s.
- The acceleration is +0.50 m/s^2.
- The time is 8.4 seconds.
Plugging these values into the equation, we get:
displacement = (0 * 8.4) + (1/2) * 0.50 * (8.4)^2
Simplifying, we have:
displacement = 0 + (1/2) * 0.50 * (70.56)
displacement = 0 + 0.25 * 70.56
displacement = 17.64
The rider's displacement is 17.64 meters.
To solve this problem, we need to use the equations of motion.
The first equation of motion is:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Since the skateboard rider starts from rest, the initial velocity (u) is 0. We are given the value of acceleration (a) as +0.50 m/s^2 and the time (t) as 8.4s.
Plugging in the values into the equation, we get:
v = 0 + (0.50 m/s^2)(8.4s)
v = 4.2 m/s
Now, we can use the second equation of motion:
s = ut + (1/2)at^2
where:
s = displacement
Since the initial velocity (u) is 0, the equation simplifies to:
s = (1/2)(0.50 m/s^2)(8.4s)^2
s = (1/2)(0.50 m/s^2)(70.56 s^2)
s = 17.64 m
Therefore, the riders displacement is 17.64 meters.