A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 22.5 m/sm/s , and the distance between them is 94.0 mm . After t1t1 = 4.00 ss , the motorcycle starts to accelerate at a rate of 5.00 m/s2m/s2 . The motorcycle catches up with the car at some time t2t2.How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words, find t2−t1t2−t1.

Express the time numerically in seconds using three significant figures.

**View Available Hint(s)**for Part B

Hint 1for Part B**.** Using a moving reference frame

Hint 2for Part B**.** Find the initial conditions for the position of the car

If the initial conditions are known at time t1t1, and the motion is one of constant acceleration, the equation for the position of the car at time t2t2 is

xc(t2)=x1,c+v1,c(t2−t1)+12ac(t2−t1)2xc(t2)=x1,c+v1,c(t2−t1)+12ac(t2−t1)2,

where xc(t)xc(t) is the positon of the car as a function of time, x1,cx1,c is its position at time t1t1, v1,cv1,cis the car's velocity at time t1t1, and acac is the car's constant acceleration. (If t1=0t1=0 , the equations become more familiar.) Let us choose a frame of reference in which at time t1t1, the motorcycle is at position x1,m=0x1,m=0. What are the values of x1,cx1,c, v1,cv1,c, and acac that you should use in the above equation?

Enter your answer in the order x1,c,v1,c,acx1,c,v1,c,ac, separated by commas as shown, in units of metersmeters, m/sm/s, and m/s2m/s2, respectively.

x1,c,v1,c,acx1,c,v1,c,ac =

94.0,22.5,0

mm, m/s,m/s, m/s2m/s2

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 Correct

Important: If you use this answer in later parts, use the full unrounded value in your calculations.

Hint 3for Part B**.** Find the initial conditions for the position of the motorcycle

If initial conditions are known at time t1t1, and the motion is one of constant acceleration, the equation for the position of the motorcycle at time t2t2 is

xm(t2)=v1,m(t2−t1)+12am(t2−t1)2xm(t2)=v1,m(t2−t1)+12am(t2−t1)2,

where the meaning of the symbols is analogous to that of Part B.2. Observe that there is no term involving the initial position, because here we have assumed that at time t1t1, the motorcycle is at position x1,m=0x1,m=0. What are the values of v1,mv1,m and amam that you should use in the above equation?

Enter your answer in the order v1,m,amv1,m,am, separated by commas as shown, in units of m/sm/s and m/s2m/s2 respectively.

v1,m,amv1,m,am =

22.5,5.00

m/sm/s, m/s2m/s2

SubmitPrevious Answers

 Correct

Important: If you use this answer in later parts, use the full unrounded value in your calculations.

Hint 4for Part B**.** Solving for the time

At time t2t2, the car and motorcycle must be at the same position, since they are side by side. This means that you can set xc(t2)xc(t2) and xm(t2)xm(t2), the positions of the car and motorcycle at time t2t2, equal to each other, and then solve for the quantity t2−t1t2−t1. You should find that some terms cancel out on either side of the equation, which will make your calculations simpler.