A bicycle has a speed of 7.5m/s at 4.3sec and a constant acceleration of 2.6m/s^2. the bicycle is at the origin (on the positive x-axis) when 1.2sec. How far from the origin is the bike at 7sec? Answer in units of m
To find the distance from the origin at a given time, we can use the equation of motion:
d = v_i * t + (1/2) * a * t^2
where:
- d is the distance from the origin,
- v_i is the initial velocity,
- t is the time elapsed, and
- a is the acceleration.
First, let's determine the initial velocity at 4.3 seconds. We know that the bicycle has a constant acceleration of 2.6 m/s^2, so we can use the equation:
v_f = v_i + a * t
where:
- v_f is the velocity at a particular time.
Rearranging the equation, we have:
v_i = v_f - a * t
Substituting the given values:
v_f = 7.5 m/s
t = 4.3 s
a = 2.6 m/s^2
v_i = 7.5 m/s - (2.6 m/s^2 * 4.3 s)
v_i = 7.5 m/s - 11.18 m/s
v_i = -3.68 m/s
The negative sign indicates that the initial velocity is in the opposite direction from the positive x-axis.
Next, let's calculate the distance at 7 seconds using the equation of motion:
d = v_i * t + (1/2) * a * t^2
Substituting the given values:
v_i = -3.68 m/s
t = 7 s
a = 2.6 m/s^2
d = -3.68 m/s * 7 s + (1/2) * 2.6 m/s^2 * (7 s)^2
d = -25.76 m + 50.54 m
d = 24.78 m
Therefore, the bike is 24.78 meters from the origin at 7 seconds.