PHYSICS: DISTANCE AND ACCELERATION

Plug in problems

1. vi = 0 m/s, t = 3 s, a = 2 m/s per s, find d

d = 9 m

2. vi = 10 m/s, t = 3 s, a = 2 m/s per s, find d

d =39 m

3. starts at rest (vi = 0 m/s), d = 50 m, t = 5 s, find acceleration

4. d = 12 m, a = 6 m/s per s, vi = 0 m/s, find t. You’ll have to take a square root at some point in your calculations. Hint: t is an integer in this problem.

t = 2s

5. d = 16 m, a = 0.5 m/s per s, vi = 0 m/s, find t. Hint: t is an integer in this problem, too.

t = 8s

Word Problems

6. A car is accelerated uniformly from a speed of 25 meters per second to a speed of 55 meters per second in 6.0 seconds. How far did the car travel in this time?

Given: vi = 25 m/svf = 55 m/st = 6.0 s

Find: d = ?

Equation: We don’t have a single equation with which we can calculate d directly. This is a 2-step problem, and there are actually two ways to do it:

A) You could use to find , then use to calculate d,

Or, B) You could use to calculate a, then to get the distance. It may be easier to do method (A), but I’ll show the solution using method (B) since that includes the new equation.

a = 5.0 m/s per s.

d= 240 m

7. A runner starts from rest and speeds up at a rate of 2.0 m/s per second. How much time does it take her to run 25.0 meters if she can continue to maintain this acceleration? You’ll have to take a square root at some point in your calculations.

t= 5.0 s

8. A plane flying at 90.0 m/s is uniformly accelerated at the rate of 3.00 m/s per second. What distance will it travel during a 10.0 second interval after the acceleration begins?

d= 1050 m

9. A particle, starting at rest, is given a constant acceleration of 7.0 m/s per second. How much time does it take for it to travel Z meters?

(Substitute your Z number for Z.)

Review and extend problems

10. An object is initially rolling down a hill at 5 m/s. It accelerates up to 11 m/s, in a time of 2.0 seconds. Find the following quantities, including units: vi, vf, ∆v, , t, d, a.

Given in the problem: vi = 5 m/svf = 11 m/st = 2.0 s

Calculated quantities:∆v = vf - vi = 11m/s – 5m/s = 6 m/s

11. An object accelerates from rest at a constant rate of acceleration. It covers a distance of 75 meters in 5.0 seconds. What was the acceleration? Also find vi, vf, ∆v, , t, and d. This one gets tricky.

Given in the problem: vi = 0 m/sd = 75 mt = 5.0 s

Calculated quantities:

vf = 30m/s

∆v = vf - vi = 30m/s – 0m/s = 30 m/s

12. An object in a lab accelerates from rest in a straight line at the low rate of 3.0 mm/s per second for a time of 2 minutes and 15 seconds. How far does it travel? (answer in MKS units)

Given in the problem: vi = 0 m/s

t = 2min15sec=135 s

Calculated quantity: d = ? (“How far?”)

d = 27m

13. An object in an explosion accelerates at 2.0 x 107 m/s per second. How much time would it take to travel 80.0 meters while accelerating at that rate? Assume the object started at rest.

Given in the problem: vi = 0 m/sd = 80.0m

Calculated quantity: t = ? (“How much time?”)

✰ 14. How much time does it take a cheetah initially running at 10 m/s to run a distance of 39 meters if accelerating at 2 m/s per s???

Given in the problem:

vi = 10 m/sd = 39m

Calculated quantity: t = ? (“How much time?”)

(without the units)39 = 10t + t2

t2 + 10t – 39 = 0

t = -13s and t = 3s. Only the positive root is possible.

t = 3s