4.3. Practice Sets: Linear Motion
Chapter Equations
[latex]a = \frac{\Delta v}{t} = \frac{v_{\large f} - v_{\large i}}{t}[/latex] (1)
[latex]S = \frac{v_{\large i} + v_{\large f}}{2} \times t[/latex] (2)
[latex]S = v_i t + \frac{1}{2} a t^2[/latex] (3)
[latex]v_f^2 = v_i^2 + 2aS[/latex] (4)
Try It!
Choose the appropriate formula from the chapter equations above for a one-step solution to the following:
- A cheetah reached a speed of [latex]35 \, \mathrm{m/s}[/latex] after covering a distance of [latex]125 \, \mathrm{m}[/latex] in [latex]9.0 \, \mathrm{s}[/latex]. What was the cheetah’s initial velocity?
- A streetcar starts from rest and travels [latex]58 \, \mathrm{m}[/latex] accelerating at a rate of [latex]0.65 \, \mathrm{m/s^2}[/latex]. How long did it take to cover the [latex]58 \, \mathrm{m}[/latex]?
- A train is decelerating at a rate of [latex]1.5 \, \mathrm{m/s^2}[/latex] to a stop. If the velocity at the time it was starting to decelerate was [latex]30 \, \mathrm{m/s}[/latex], find the stopping distance.
Practice
- A penguin slides down a glacier starting from rest and accelerates at a rate of [latex]7.6 \, \text{m/s}^2[/latex]. If it reaches the bottom of the hill travelling [latex]15 \, \text{m/s}[/latex], how long does it take to get to the bottom?
Answer:[latex]1.97\, \text{s}[/latex] - A car slows from [latex]45 \, \text{m/s}[/latex] to [latex]30 \, \text{m/s}[/latex] in [latex]6.2 \, \text{s}[/latex]. How far does it travel in that time?
Answer:[latex]232.5 \, \text{m}[/latex] - A cyclist speeds up from his [latex]8.45 \, \text{m/s}[/latex] pace. As he accelerates, he travels [latex]325 \, \text{m}[/latex] in [latex]30 \, \text{s}[/latex]. What is his final velocity?
Answer:[latex]13.2 \, \text{m/s}[/latex] - If a car was going at a speed of [latex]35 \, \text{m/s}[/latex] when it starts to decelerate at a rate of [latex]4.64 \, \text{m/s}^2[/latex] to a complete stop, how long did it take for the car to stop?
Answer:[latex]7.5 \, \text{s}[/latex] - A train decelerates at a rate of [latex]3.5 \, \text{m/s}^2[/latex] to a stop in [latex]150 \, \text{m}[/latex]. What was the train’s speed when it started to decelerate?
Answer:[latex]32.4 \, \text{m/s}[/latex]
Challenge Question(s)
Try out the two challenge questions below. Choose the best answer.
Text Version of the Challenge Question(s)
- 1. A drag-racing car accelerates from rest at a rate of [latex]11.0 \, \text{m/s}^2[/latex] for a distance of [latex]120 \, \text{m}[/latex]. The car coasts for [latex]0.75 \, \text{s}[/latex]; then the driver brakes and opens the parachute to decelerate until the end of the track. If the total length of the track is [latex]200 \, \text{m}[/latex], what is the minimum deceleration rate to stop before reaching the end of the track?
Answer:[latex]-11.8 \, \text{m/s}^2[/latex]
- 2. A driver is going at a constant speed of [latex]28.0 \, \text{m/s}[/latex]. She sees a moose jump onto the road [latex]56.0 \, \text{m}[/latex] in front of her. The driver brakes and decelerates at [latex]7.5 \, \text{m/s}^2[/latex], stopping in front of the moose. What is the driver’s reaction time? (In other words, how long did it take the driver to react to the event prior to decelerating?)
Answer:[latex]0.13 \, \text{s}[/latex]
