You give a toy car an initial velocity of 1.10 m/s directed up a ramp. The car t

Question

You give a toy car an initial velocity of 1.10 m/s directed up a ramp. The car takes a total of 10.00 s to roll up the ramp and then roll back down again into your hand. Assume that you catch the car at the same point from which you released it, and that the acceleration is constant through the entire motion.
(a) Determine the magnitude of the car's acceleration.
m/s2
(b) Determine the total distance traveled by the car in this 10.00 second period.
m


and


On August 16, 1960, Joe Kittinger of the United States Air Force jumped from a helium balloon from a height of 102,800 feet. After being in free fall for 4 minutes and 36 seconds, and falling for 85,300 feet, he opened his parachute and eventually landed safely on the ground. To analyze this situation, we will assume that Kittinger's initial velocity was zero, and that his acceleration was constant throughout the free fall. (This was most certainly not the case, but it gives us some idea about the motion.) Note the units we're looking for in the questions below.
(a) What was the magnitude of the acceleration during the free fall?
m/s2
(b) At the end of the free fall part of the motion, what was Kittinger's speed?
m/s

Explanation / Answer

hello skilight,

toy car problem

1. since we need to relate velocity, acceleration, and time, we will use the equation, v=v0+at

where v is the final velocity,

v0 is the initial velocity,

a is the acceleration,

and t is time.

2. we assume that the toy car does not experience friction, it will have the same speed at the point it is released and after it rolls back down the ramp (1.10m/s).

3. however the car is traveling in opposite directions at those two points, therefore

v0=+1.10 m/s

v=-1.10 m/s

*the positive direction is upward along the ramp

4. it takes 10 seconds for the car to travel up and down the ramp

t=10s

5. we substitute these values into the equation.

(-1.10)=(1.10)+a(10)

6. solve for a.

a=-.22 m/s2

7. the distance traveled is given by the equation,

d=v0t+(1/2)at2

where d is the distance traveled,

v0 is the inital velocity,

a is the acceleration,

and t is time.

8. we know that it takes exactly half the time and half the distance to travel up the ramp. therefore,

t=5 seconds

9. substitute our values into the equation

d=(1.10)(5)+(1/2)(-.22)(52)

10. solve for d

d=2.75 m

11. since d is the distance the toy car travels up the ramp, the total distance is given by 2d.

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