Question

4. Suppose a police car is driving along at a leisurely 18.0 m/s. When someone speeding flies by the police car, the cop turns on their flashing lights and accelerates at 4.00 m/s2 for the next 4.25 s, until the police car is driving at the same speed as the speeder. How fast is the speeder is going in m/s? 5. Francisca is a baseball player for the Umatilla Ultraviolet Catastrophes. Her team is playing against the Pittsburgh Planckians. When Francisca is at bat, she hits the ball into the outfield, where it takes If you haven't watched much baseball, the important thing to know for this problem is that the batter is trying to run from home, to first base, to second base, to third base, and then to home again without the other team stopping her. There are ninety feet of distance between each base. some bounces that confuse the defenders. She sprints the 90 feet from home to first base in 4 seconds, pauses for 1 second to look at what the defenders are doing, then sprints to second base, third base, and then to home in an additional 13 seconds, where she stops to celebrate her inside-the-park homerun. What is Francisca's average velocity and average acceleration throughout this process? (Hint: Don't just start plugging numbers into things. Think carefully and cleverly. Physicists love being lazy and finding easier ways to solve problems.)

Could I get help with questions 4 and 5. Im confused on which formula to use

Answer 1

4) The details given in the question are the following:

Initial velocity of the police car , u = 18 m/s

Acceleration of the car , a = 4 m/s²

Time , t = 4.25 s

Let v be the final velocity of the police car after 4.25 seconds

Then using first equation of motion, we have

v = u + at

substituting the values

v = 18 + (4×4.25) = 18 + 17 = 35 m/s

It is said in the question that after 4.25 seconds velocity of the speeder and police car are same.

Hence velocity of the speeder = v = 35 m/s

5) This is a tricky question and answer is very simple

Average velocity is the rate at which the position of an object changes in one second of time.

Average velocity = Total displacement / total time.

Fransisca is initially at home and she reaches back to the home finally.

Hence her displacement is zero.

Total time = 4+1+13 = 18 s

Because displacement is the straight line distance between initial and final position.

So Average velocity = 0/18 = 0 m/s.

Average acceleration = (final velocity - initial velocity ) / time taken for change in velocity.

Initial velocity = 0 m/s since player is initially at rest in home.

Final velocity = 0m/s since player stops at home when she reaches back there.

Time = 18 s

Average acceleration = 0/18 = 0 m/s²