An object accelerates uniformly from rest at a rate of 2 m/s2 for 3 s and then 5 m/s2 for 15 s. Find its final velocity?
Do it in two parts.
Or, find the total impulse given
F=ma
1) F=m*2
2) F=m*5
Impulse=2m*3+5m*15
set that equal to the change in momentum mV, and solve for V
2m/s
To find the final velocity of the object, we can use the equation for uniformly accelerated motion:
v = u + at
where:
v = final velocity
u = initial velocity (in this case, it starts from rest, so u = 0)
a = acceleration
t = time taken
First, let's calculate the velocity after the first 3 seconds:
v1 = u + a1 * t1
where:
a1 = acceleration for the first part of the motion (2 m/s^2)
t1 = time for the first part of the motion (3 s)
Plugging in the values, we get:
v1 = 0 + 2 * 3
v1 = 6 m/s
Now, let's calculate the velocity after the next 15 seconds:
v2 = u + a2 * t2
where:
a2 = acceleration for the second part of the motion (5 m/s^2)
t2 = time for the second part of the motion (15 s)
Plugging in the values, we get:
v2 = v1 + a2 * t2
v2 = 6 + 5 * 15
v2 = 6 + 75
v2 = 81 m/s
Therefore, the final velocity of the object is 81 m/s.