Question

A pair of particles a and b are moving in the same direction along a straight path. particle a is accelerating at 2.5 m s − 2 . when its velocity is 1.5 m s − 1 , it is passed by particle b which is moving at 7.5 m s − 1 and accelerating at 1 m s − 2 . how long until a passes b ?

Answer 1

Particle a will pass particle b after 6 seconds and when particle b has traveled 63 meters.

Step-by-step explanation:

To determine how long it takes for particle a to pass particle b, we can first calculate the time it takes for particle b to reach the same velocity as particle a (1.5 m/s). The equation for particle b's velocity as a function of time is v(t) = 7.5 + 1t. Setting this equal to 1.5 m/s, we can solve for t: 1.5 = 7.5 + 1t. Solving this equation gives us t = -6. The negative value is not physically meaningful, so we discard it. Therefore, it takes particle b 6 seconds to reach the velocity of particle a.

Next, we can calculate the distance particle b travels during this time. We use the equation for displacement: s = ut + 0.5at², where u is the initial velocity, t is the time, and a is the acceleration. Plugging in the values for particle b (u = 7.5 m/s, t = 6 s, a = 1 m/s²), we find s = 7.5(6) + 0.5(1)(6²) = 45 + 18 = 63 meters. Therefore, particle a will pass particle b after 6 seconds and when particle b has traveled 63 meters.