Question

Cars A and B travel along the same straight track. Car A is located at position s1 at clock reading t1 and it maintains a constant speed of v1. Car B is located at position s2 < s1 at clock reading t2, and it maintains a constant speed of v2 > v1. Find an expression for the clock reading at which car B will overtake car A. Find also an expression for the position at which car B overtakes car A. Evaluate your expressions for the values s1 = 0.75 meters, t1 = 0.00 seconds, v1 = 0.38 m s−1 , s2 = 0.0 meters, t2 = 0.08 seconds, and v2 = 0.78 m s−1 .

Answer 1

Answer:

a) $t=\frac{S1-V1*t1 - S2 + V2*t2}{V2-V1}$

b) $X = S2 - V2*t2 + V2*\frac{S1-V1*t1 - S2 + V2*t2}{V2-V1}$

c) t = 2.031s      X = 1.52m

Explanation:

Let X1 be position of car A as a function of time and X2 be the position of car B as a function of time:

X1 = Xo1 + V1*t     If we evaluate this expression at t=t1

S1 = Xo1 + V1*t1    Solving for Xo1 we get its initial position at t=0:

Xo1 = S1 - V1*t1    

Similarly for car B:

Xo2 = S2 - V2*t2

Now, to find the instant when car B overtakes car A:

X1 = X2   Replacing their functions in time:

(S1 - V1*t1) + V1*t  = (S2 - V2*t2) + V2*t   Solving for t:

$t=\frac{S1-V1*t1 - S2 + V2*t2}{V2-V1}$   This is the instant when B reaches A

If we replace this expression in either X1 or X2 expression, we get that position:  X1 = X2

$X1 = X2 = X = S2 - V2*t2 + V2*\frac{S1-V1*t1 - S2 + V2*t2}{V2-V1}$

If we evaluate these two expressions with the given values:

t = 2.031s  and   X = 1.52m