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Magazine Chapter 1: Q2-30E (page 1)
A cat walks in a straight line, which we shall call the \(x\)-axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat鈥檚 motion and construct a graph of the feline鈥檚 velocity as a function of time (Fig. E2.30). (a) Find the cat鈥檚 velocity at \(t = 4.0\,s\) and at \(t = 7.0\,s\).
Short Answer
Hence, the required velocities are
\({v_{4\,s}} = 2.68{\rm{ cm/s and }}{v_{7\,s}} = 1.31{\rm{ cm/s}}\).
Step by step solution
Velocity and Acceleration
The measurement of change of displacement with respect to time is known as velocity, whereas that of velocity with respect to time is known asacceleration.
Examine the given graph(a)
The given graph for cat's velocity as a function of time is:
From the graph, the acceleration can be evaluated as:
\(a = \frac{{\Delta v}}{{\Delta t}} = \frac{{0 - 8}}{{6 - 0}} \approx - 1.33{\rm{ cm/}}{{\rm{s}}^2}\)
Now, using \({v_t} = {v_0} + at\), at \(t = 4\,s\), the velocity of cat is:
\(\begin{aligned}{v_{4\,s}} = 8 - \left( {1.33 \times 4} \right)\\ = 2.68{\rm{ cm/s}}\end{aligned}\)
Find velocity
Similarly,at\(t = 7\,s\), the velocity of cat is:
\(\begin{aligned}{v_{7\,s}} = 8 - \left( {1.33 \times 7} \right)\\ = 1.31{\rm{ cm/s}}\end{aligned}\)
Hence, the required velocities are
\({v_{4\,s}} = 2.68{\rm{ cm/s and }}{v_{7\,s}} = 1.31{\rm{ cm/s}}\).
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