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's motion and construct a graph of the feline's velocity as a function of time (Fig. E$2.30$). What is the cat's acceleration at $t=3.0$ s? At $t=6.0$ s? At $t=7.0$ s?

A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the driver accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of $20$ m/s ($45$ mi/h) when it reaches the end of the $120$-m-long ramp. How much time does it take the car to travel the length of the ramp?

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's motion and construct a graph of the feline's velocity as a function of time (Fig. E$2.30$). What distance does the cat move during the first $4.5$ s? From $t=0$ to $t=7.5$ s?

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's motion and construct a graph of the feline's velocity as a function of time (Fig. E$2.30$). Find the cat's velocity at $t=4.0$ s and at $t=7.0$ s.

A small block has constant acceleration as it slides down a frictionless incline. The block is released from rest at the top of the incline, and its speed after it has traveled $6.80$ m to the bottom of the incline is $3.80$ m/s. What is the speed of the block when it is $3.40$ m from the top of the incline?

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's motion and construct a graph of the feline's velocity as a function of time (Fig. E$2.30$). Assuming that the cat started at the origin, sketch clear graphs of the cat's acceleration and position as functions of time.

At launch a rocket ship weighs $4.5$ million pounds. When it is launched from rest, it takes $8.00$ s to reach $161$ km/h; at the end of the first $1.00$ min, its speed is $1610$ km/h. What is the average acceleration (in m/s²) of the rocket (i) during the first $8.00$ s and (ii) between $8.00$ s and the end of the first $1.00$ min?