Answer:
a) 6.46 s
b) 73.0 m
c) 22.6 m/s, 26.7 m/s
Explanation:
The position can be found with constant acceleration equation:
x = x₀ + v₀ t + ½ at²
where x is the final position,
x₀ is the initial position,
v₀ is the initial velocity,
a is the acceleration,
and t is the time.
For John:
x₀ = 0 m
v₀ = 0 m/s
a = 3.50 m/s²
For Peter:
x₀ = 0 m
v₀ = 0 m/s
a = 4.90 m/s²
John's position at time t is:
x = 0 + (0) t + ½ (3.50) t²
x = 1.75 t²
Peter starts 1 second after John. Peter's position at time t−1 is:
x = 0 + (0) (t−1) + ½ (4.90) (t−1)²
x = 2.45 (t−1)²
When Peter overtakes John, they have the same position:
1.75 t² = 2.45 (t−1)²
1.75 t² = 2.45 (t² − 2t + 1)
1.75 t² = 2.45 t² − 4.90 t + 2.45
0 = 0.70 t² − 4.90 t + 2.45
0 = 2 t² − 14 t + 7
t = [ 14 ± √(169 − 4(2)(7)) ] / 4
t = 0.54, 6.46
Since t > 1, Peter overtakes John 6.46 seconds after the race starts, which means he drives for 5.46 seconds.
The distance Peter travels is:
x = 2.45 (6.46 − 1)²
x = 73.0
Peter travels 73.0 meters.
The speed that John reaches is:
v = (3.50 m/s²) (6.46 s)
v = 22.6 m/s
The speed that Peter reaches is:
v = (4.90 m/s²) (5.46 s)
v = 26.7 m/s
