A point moves rectilinearly in one direction. Fig. 1.1 shows the distance s traversed by the point as a function of the time Using the plot find:

(a) the average velocity of the point during the time of motion;

(b) the maximum velocity;

(c) the time moment t0 at which the instantaneous velocity is equal to the mean velocity averaged over the first t0 seconds.

Solution:

(a) Sought average velocity

$$<v>=\frac{s}{t}=\frac{200\,cm}{20\,s}=10\,cm/s$$

(b) For the maximum velocity,  $$\frac{ds}{dt}$$ should be maximum. From the figure  $$\frac{ds}{dt}$$ is maximum for all points on the line ac, thus the sought maximum velocity becomes average velocity for the line ac and is equal to:

$$\frac{bc}{ab}=\frac{100\,cm}{4\,s}=25\,cm/s$$

(c) Time t0 should be such that corresponding to it the slope  $$\frac{ds}{dt}$$ should pass through the point O (origin), to satisfy the ralationship  $$\frac{ds}{dt}=\frac{s}{{{t}_{0}}}$$. From figure the tangent at point d passes through the origin and thus corresponding time  $$t={{t}_{0}}=16\,s$$.

## Kinematics!

#### A motorboat going downstream overcame a raft at a point A; τ=60min later it turned back and after some time passed the raft at a distance ℓ=6.0kmfrom the point Find the flow velocity assuming the duty of the engine to be constant

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