The velocity of a vehicle is measured at two distinct points in time and found to be 30 m/s at 1.0 s and 10 m/s at 2.0 s. Find the acceleration (in m/s2) and initial velocity (in m/s) to complete the equation of motion for the velocity of the vehicle.
v(t) = t +
Round your answers to the nearest whole number.
To find the acceleration (a) and initial velocity (u), we will use the equation of motion for velocity:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
We are given the following information:
v(1.0s) = 30 m/s
v(2.0s) = 10 m/s
Let's first find the acceleration (a). To do this, we can subtract the initial velocity from the final velocity and divide it by the time elapsed:
a = (v - u) / t
Substituting the given values:
a = (10 m/s - 30 m/s) / (2.0 s - 1.0 s)
= (-20 m/s) / (1.0 s)
= -20 m/s²
Therefore, the acceleration is -20 m/s².
Now, let's find the initial velocity (u). We can rearrange the equation of motion to solve for u:
v = u + at
Rearranging it, we get:
u = v - at
Substituting the known values:
u = 30 m/s - (-20 m/s² * 1.0 s)
= 30 m/s - (-20 m/s)
= 30 m/s + 20 m/s
= 50 m/s
Therefore, the initial velocity is 50 m/s.
Now we can complete the equation of motion for the velocity of the vehicle:
v(t) = t + 50
Therefore, the equation of motion for the velocity of the vehicle is:
v(t) = t + 50.
acceleration=changeInVelocity/time=(10-30)/(2-1) = -20m/s^2
vf=vi+at
10=vi-20*2
vi=50m/s