In professional baseball, the pitching distance of $60$ feet $6$ inches is the distance from the front of the pitcher's plate (or rubber) to the rear of the home plate. $(a)$ Assuming that a $95 \mathrm{mi} / \mathrm{h}$ fastball travels that full distance horizontally, what is its flight time, which is the time a batter must judge if the ball is "hittable" and then swing the bat? $(b)$ Research indicates that even an elite batter cannot track the ball for the full flight and yet many players have described seeing the ball-bat collision. One explanation is that the eyes track the ball in the early part of the flight and then undergo a predictive saccade in which they jump to an anticipated point later in the flight. A saccade suppresses vision for $20 \mathrm{~ms}$. How far in feet does the fastball travel during that interval of no vision?

When startled, an armadillo will leap upward. Suppose it rises 0.544 m in the first 0.200 s. What is its initial speed as it leaves the ground?

If the position of a particle is given by $x = 20t - 5t^3$, where $x$ is in meters and $t$ is in seconds, when, if ever, is the particle’s velocity zero?

If a particle’s position is given by $x = 4- 12t + 3t^2$ (where t is in seconds and x is in meters), what is its velocity at t = 1 s?

A rocket-driven sled running on a straight, level track is used to investigate the effects of large accelerations on humans. One such sled can attain a speed of $1600 \text{ km/h}$ in $1.8 \text{ s}$, starting from rest. Find the distance traveled.?

A rocket-driven sled running on a straight, level track is used to investigate the effects of large accelerations on humans. One such sled can attain a speed of $1600 \text{ km/h}$ in $1.8 \text{ s}$, starting from rest. Find the acceleration (assumed constant) in terms of g ?

A simple device for measuring your reaction time. It consists of a cardboard strip marked with a scale and two large dots. A friend holds the strip vertically, with thumb and forefinger at the dot on the right. You then position your thumb and forefinger at the other dot, being careful not to touch the strip. Your friend releases the strip, and you try to pinch it as soon as possible after you see it begin to fall. The mark at the place where you pinch the strip gives your reaction time.

250 ms ? (For example, should the 100 ms marker be 2 times as far from the dot as the 50 ms marker? If so, give an answer of 2 times. Can you find any pattern in the answers?)

A simple device for measuring your reaction time. It consists of a cardboard strip marked with a scale and two large dots. A friend holds the strip vertically, with thumb and forefinger at the dot on the right. You then position your thumb and forefinger at the other dot, being careful not to touch the strip. Your friend releases the strip, and you try to pinch it as soon as possible after you see it begin to fall. The mark at the place where you pinch the strip gives your reaction time.

200, and

A simple device for measuring your reaction time. It consists of a cardboard strip marked with a scale and two large dots. A friend holds the strip vertically, with thumb and forefinger at the dot on the right. You then position your thumb and forefinger at the other dot, being careful not to touch the strip. Your friend releases the strip, and you try to pinch it as soon as possible after you see it begin to fall. The mark at the place where you pinch the strip gives your reaction time.

150,

A simple device for measuring your reaction time. It consists of a cardboard strip marked with a scale and two large dots. A friend holds the strip vertically, with thumb and forefinger at the dot on the right. You then position your thumb and forefinger at the other dot, being careful not to touch the strip. Your friend releases the strip, and you try to pinch it as soon as possible after you see it begin to fall. The mark at the place where you pinch the strip gives your reaction time.

100

The given figure shows a simple device for measuring your reaction time. It consists of a cardboard strip marked with a scale and two large dots. A friend holds the strip vertically, with thumb and forefinger at the dot on the right in Fig. 2-37. You then position your thumb and forefinger at the other dot (on the left in given figure), being careful not to touch the strip. Your friend releases the strip, and you try to pinch it as soon as possible after you see it begin to fall. The mark at the place where you pinch the strip gives your reaction time. How far from the lower dot should you place the $50.0 \mathrm{~ms}$ mark?

The mentioned figure gives the acceleration $a$ versus time $t$ for a particle moving along an $x$ axis. The $a$-axis scale is set by $a_s=$ $12.0 \mathrm{~m} / \mathrm{s}^2$. At $t=-2.0 \mathrm{~s}$, the particle's velocity is $7.0 \mathrm{~m} / \mathrm{s}$. What is its velocity at $t=6.0 \mathrm{~s} ?$

A particle’s acceleration along an x axis is a = 5.0 t, with t in seconds and a in meters per second squared. At t = 2.0 s, its velocity is +17 m/s. What is its velocity at t = 4.0 s?

Do the three lines $x_{1}-4 x_{2}=1,2 x_{1}-x_{2}=-3$, and $-x_{1}-3 x_{2}=4$ have a common point of intersection? Explain.