Answer:
At t = 5 s, the velocity is 4.5 m/s, and for t > 5 s, it will continue increasing 0.5 m/s each second
Explanation:
We can find the velocity of the cart after t = 5 seconds using the equation:
v = u +at
where
v is the final velocity
u is the initial velocity
t is the time
a is the acceleration
For the cart in the problem,
[tex]a=0.50 m/s^2\\u = 2.0 m/s[/tex]
Substituting t = 5 s, we find the velocity after 5 seconds:
[tex]v=2.0+(0.50)(5)=4.5 m/s[/tex]
And after t > 5 s, the cart will continue accelerating, increasing its velocity by 0.50 m/s each second.
Explanation:
The given data is as follows.
a = 0.5 [tex]m/s^{2}[/tex], initial velocity = 2 m/s
After sometime, the inclined velocity will be equal to 0. Now, using the equation of motion as follows.
[tex]V^{o}_{f} - V_{o}[/tex] = at
t = [tex]\frac{-V_{o}}{-a}[/tex]
= [tex]\frac{2 m/s}{0.5 m/s^{2}}[/tex]
= 4 s
And, at t = 4 s, [tex]v_{f}[/tex] = 0 and the cart starts to roll down the incline.
So, for t > 5 sec we assume that t = 6 sec.
Hence, [tex]v_{f} - v_{o} = at[/tex]
[tex]v_{f} = 0.5 m/s^{2} \times 6 sec[/tex]
[tex]v_{f}[/tex] = 3 m/s
This means that the cart is travelling in -x direction and it is speeding at t > 5 sec.
