A trolley of mass 2kg accerates from rest across a rough surface at 2,5m.s.It experiences a frictional force of 3N.Calculate the velocity of trolley after 4s and the distance travelled by the trolley in 4s
To calculate the velocity of the trolley after 4 seconds and the distance traveled by the trolley in 4 seconds, we can use the equations of motion.
First, we need to determine the net force acting on the trolley.
The net force can be found by subtracting the frictional force from the force causing acceleration. In this case, the force causing acceleration is unknown, so we can calculate it using Newton's second law:
Net force = mass × acceleration
Given that the mass of the trolley is 2 kg and the acceleration is 2.5 m/s², we can calculate the force causing acceleration:
Force causing acceleration = Net force / mass
Therefore,
Force causing acceleration = (2 kg × 2.5 m/s²) = 5 N
Next, we can determine the net force by subtracting the frictional force from the force causing acceleration:
Net force = Force causing acceleration - Frictional force
Given that the frictional force is 3 N, we can calculate the net force:
Net force = 5 N - 3 N = 2 N
Now, we can use the equation of motion to calculate the final velocity of the trolley after 4 seconds:
v = u + at
where:
v = final velocity
u = initial velocity (which is zero in this case)
a = acceleration
t = time
Given that the initial velocity is zero, the acceleration is 2.5 m/s², and the time is 4 seconds, we can calculate the final velocity:
v = (0) + (2.5 m/s² × 4 s) = 10 m/s
Therefore, the final velocity of the trolley after 4 seconds is 10 m/s.
To calculate the distance traveled by the trolley in 4 seconds, we can use another equation of motion:
s = ut + 0.5at²
where:
s = distance traveled
u = initial velocity (zero in this case)
t = time
a = acceleration
Given that the initial velocity is zero, the time is 4 seconds, and the acceleration is 2.5 m/s², we can calculate the distance traveled:
s = (0) + (0.5 × 2.5 m/s² × (4 s)²) = 20 m
Therefore, the distance traveled by the trolley in 4 seconds is 20 meters.