Question

Kathy tests her new sports car by racing with Stan, an experienced racer. Both start from rest, but Kathy leaves the starting line 1.00 s after Stan does. Stan moves with a constant acceleration of 3.4 m/s2 while Kathy maintains an acceleration of 4.49 m/s2. (a) Find the time at which Kathy overtakes Stan. 6.7 Correct: Your answer is correct. seenKey 6.7 s from the time Kathy started driving

Answer 1

time at which Kathy overtakes Stan is 6.70 sec

Step-by-step explanation:

given data

time = 1 sec

acceleration= 3.4 m/s²

acceleration = 4.49 m/s²

to find out

the time at which Kathy overtakes Stan

solution

we consider here travel time for kathy = t1

and travel time for stan is = t2

and we know initial velocity = 0

so

t1 = 1 + t2

and distance travel equation by kinematic is

d1 = ut +
`(1)/(2)` at²

d1 = 0+
`(1)/(2)` 4.49 (t2)² ................1

and

d2 = 0 +
`(1)/(2)` 3.4 (1+t2)² ..................2

and when overtake distance same so from equation 1 and 2

`(1)/(2)` 4.49 (t2)² =
`(1)/(2)` 3.4 (1+t2)²

t2 = 6.703828 sec

so time at which Kathy overtakes Stan is 6.70 sec