Calculus

Displacement, Velocity, Acceleration

Finding Displacement given Velocity

         

A particle moves along the xx-axis with velocity v(t)=30t290t+60v(t)=30t^2-90t+60 at time tt. Find the total distance covered between time t=0t=0 and time t=5.t=5.

The above is the velocity-time graph of a runner. How far does this runner travel for 1616 seconds?

The figure’s vertical scaling is set by vs=8.0 m/s. v_{s} = 8.0 \text{ m/s.}

A train starts from station AA and arrives at station BB in 66 minutes. If the velocity of the train in m/min\text{m/min} is v(t)=24t2(6t),v(t) = 24t^2(6-t), what is the distance between the two stations AA and B?B?

Sam throws a ball straight upward at a speed of 30 m/s30 \text{ m/s} from the edge of a cliff 19 m19 \text{ m} high, as shown in the above diagram. If the the velocity of the ball tt seconds after the ball leaves his hand is v=3010tv=30-10t (in m/s\text{m/s}), what is the distance of the ball from the ground 33 seconds after the ball leaves his hand?

Two points PP and QQ start at the origin and move from the origin at the same time along the xx-axis. At time t>0t>0, PP and QQ have velocities of sin(πt)\sin (\pi t) and 2sin(2πt)2\sin (2\pi t), respectively. If PP and QQ first meet again after mn\frac{m}{n} seconds, where mm and nn are positive co-prime integers, what is the value of m+nm+n?

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