Question

david is driving a steady 21.0 m/s when he passes tina, who is sitting in her car at rest. tina begins to accelerate at a steady 2.30 m/s2 at the instant when david passes.

Answer 1

Step-by-step explanation:

To find the time taken by Tina to catch up with David, we can use the equation for relative velocity:

v_rel = v_david - v_tina

where v_david is the velocity of David (21.0 m/s) and v_tina is the velocity of Tina. At the instant when David passes, Tina is at rest, so v_tina = 0 m/s. Hence,

v_rel = 21.0 m/s - 0 m/s = 21.0 m/s

Next, we can use the equation for velocity:

v = v0 + at

where v0 is the initial velocity of Tina (which is 0 m/s), a is the acceleration of Tina (2.30 m/s^2), and t is the time elapsed.

Since the relative velocity is 21.0 m/s, we can equate v_rel to the difference between the final velocity of Tina and the initial velocity of David:

v_rel = v_tina - v_david

Solving for v_tina and substituting the values, we get:

v_tina = v_rel + v_david = 21.0 m/s + 21.0 m/s = 42.0 m/s

Finally, we can use the equation for velocity to find the time elapsed:

t = (v_tina - v0) / a = (42.0 m/s - 0 m/s) / (2.30 m/s^2) = 18.26 s

Hence, it will take Tina 18.26 seconds to catch up with David.