Relative Motion: How to Calculate Distance When One Overtakes Another
How can we calculate the distance between two moving objects when one overtakes the other?
Given data: Fred in car A passes the off licence at a steady speed of 72km/h. 10 seconds later, Joey in car B moves off from rest from the off licence in pursuit of Fred. Joey accelerates at 2 ms^-2. How far will they both be from the off licence when Joey overtakes Fred? (746.4 m)
Calculation of Distance When Joey Overtakes Fred:
Initially, Fred in car A is travelling at a speed of 72km/h, which needs to be converted to meters per second. Therefore, Fred's speed (s₁) is 72km/h * (1000m/1km) * (1h/3600s) = 20 m/s.
Explanation:
Joey in car B accelerates at 2 m/s^2 from rest. The time it takes for Joey to reach Fred's speed is determined by t₁ = s₁/a = 20 m/s / 2 m/s^2 = 10 seconds. Taking into account Fred's initial head start of 10 seconds, when Joey reaches Fred's speed, 20 seconds have passed and Fred has covered a distance of d₁ = s₁ * t = 20 m/s * 20 s = 400 meters.
Since both cars are now travelling at the same speed, Joey will overtake Fred when he covers the same distance as Fred. Given that Joey's acceleration is 2 m/s^2, the distance covered by Joey (d) is calculated using the equation of motion: d = u*t + 0.5*a*t^2. With Joey's initial speed (u) being 0, the distance is d = 0.5 * 2 m/s^2 * 20^2 s = 400 meters.
Final Answer:
When Joey overtakes Fred, they will both be located at a distance of 400m + 400m = 800 meters from the off licence.
Understanding Relative Motion:
Relative motion is a concept that deals with the motion of an object concerning another moving or stationary object. When calculating the distance between two moving objects as one overtakes the other, it is crucial to consider their speeds, accelerations, and the time taken for overtaking to occur.
In the given scenario, Fred and Joey are travelling in cars A and B, respectively. Fred's initial speed and Joey's acceleration are provided to determine the distance between them when Joey overtakes Fred. By converting Fred's speed to meters per second and accounting for the time elapsed with Joey's acceleration, the calculated distance at the point of overtaking is 800 meters.
Understanding the relative motion between two objects in motion allows for the precise calculation of distances and positions at specific points in time. By utilizing equations of motion and considering initial conditions, the relationship between the objects' speeds and accelerations can be analyzed effectively.