# Kinematics

(Please see attached file for figures)

1. You are driving down the highway late one night at 20m/s when a deer steps onto the road 35m in front of you. Your reaction time before stepping on the brakes is 0.50 s, and the maximum deceleration of your car is 10m/s^2. How much distance is between you and the deer when you come to a stop?

When you press the brakes at time t2 =0.5 s after seeing the deer, the acceleration changes. You will need to consider the two time intervals (before and after the brakes are pressed) separately, since they have different accelerations. Let t1 =0s be the moment when you see the deer and x1= 0m be your position at that moment. Let t2 and x2 be the time and position when you press the brakes, and let t3 and x3 be the time and position when you finally come to rest.

VARIABLES: ax, xi, xf, vi, vf, Δt

A. Sort the variables for the period from t1 =0s to t2 =0.5s based on whether their values are known or unknown.

Known=

Unknown=

B. Sort the variables for the period from t2 =0.5s until the car comes to rest, at time t3, based on whether their values are known or unknown.

Known=

Unknown=

2. A rural mail carrier is driving slowly, putting mail in mailboxes near the road. He overshoots one mailbox, stops, shifts into reverse, and then backs up until he is at the right spot. The velocity graph of the figure represents his motion (see attachment)

A. Draw the mail carrier's position-versus-time graph. Assume that x= 0m at t= 0s.

B. What is the position of the mailbox?

3. A bicyclist has the position-versus-time graph shown in the figure (see attachment).

A.What is the bicyclist's velocity at t= 10s?

B. What is the bicyclist's velocity at t= 25s?

C. What is the bicyclist's velocity at t= 35s?

4. A car starts from xi = 13m at ti = 0 and moves with the velocity graph shown in figure (see attachment).

A. What is the object's position at t= 3s?

B. What is the object's position at t= 4s?

C. Does this car ever change direction?

5. When jumping, a flea reaches a takeoff speed of 1.2m/s over a distance of 0.54mm.

A. What is the flea's acceleration during the jump phase?

B. How long does the acceleration phase last?

C. If the flea jumps straight up, how high will it go? (Ignore air resistance for this problem; in reality, air resistance plays a large role, and the flea will not reach this height.)

6. For each motion diagram shown in the figure, determine the sign (positive or negative) of the acceleration.

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#### Solution Summary

Detailed step by step solutions with figures provided.