A car accelerates from rest with a uniform acceleration of 1.7m/s for 10secs., its acceleration then reduces by 0.3m/s for 20secs. of the motion it then maintains the speed attained for another 20secs. after which it decelerates to rest within 10secs. hence calculate the magnitude of the velocity after 10secs. and 30secs.
To calculate the magnitude of the velocity after 10 seconds and 30 seconds, we can break down the motion of the car into individual segments and calculate the velocity at the end of each segment.
Given:
Initial velocity, u = 0 (as the car starts from rest)
Uniform acceleration, a1 = 1.7 m/s² (for the first 10 seconds)
Acceleration decrease, Δa = -0.3 m/s² (for the next 20 seconds)
Constant speed, v1 = v2 (for the next 20 seconds)
Deceleration, a2 = -v1/10 (to decelerate to rest in 10 seconds)
Segment 1: 0 - 10 seconds (uniform acceleration)
Using the formula: v = u + at
v1 = 0 + a1*t1
v1 = 1.7 * 10 = 17 m/s
Segment 2: 10 - 30 seconds (decreasing acceleration)
Using the formula: v = u + at
v2 = v1 + (a1 + Δa)*t2
v2 = 17 + (1.7 + (-0.3)) * 20 = 17 + (1.4) * 20 = 17 + 28 = 45 m/s
So, the magnitude of the velocity after 10 seconds is 17 m/s, and after 30 seconds is 45 m/s.
To calculate the magnitude of the velocity after 10 seconds and 30 seconds, we need to break down the motion into different stages and then calculate the velocity at each stage.
Let's analyze each stage of the motion:
Stage 1: Accelerating from rest with a uniform acceleration of 1.7 m/s^2 for 10 seconds.
Using the formula for velocity during uniform acceleration:
v = u + at
where:
v = final velocity
u = initial velocity (in this case, 0 m/s)
a = acceleration (1.7 m/s^2)
t = time (10 seconds)
v1 = 0 + (1.7 × 10) [Substituting the values into the formula]
v1 = 17 m/s [Calculating the result]
So, after 10 seconds, the magnitude of the velocity is 17 m/s.
Stage 2: Acceleration reduces by 0.3 m/s every second for 20 seconds.
In this stage, the acceleration changes every second, so we need to calculate the velocity for each second and add them up.
For the first second:
v2_1 = v1 + a × t [Using the formula for velocity during uniform acceleration]
= 17 + (1.7 - 0.3) × 1 [Substituting the values into the formula]
= 17 + 1.4
= 18.4 m/s
For the second second:
v2_2 = v2_1 + a × t
= 18.4 + (1.7 - 0.6) × 1
= 18.4 + 1.1
= 19.5 m/s
Continuing this process for 20 seconds, we find that:
v2 = 19.5 m/s + 19.4 m/s + ... + 38.3 m/s [Adding up the velocities for each second]
= 583.2 m/s
So, after 30 seconds, the magnitude of the velocity is 583.2 m/s.
Therefore, the magnitude of the velocity after 10 seconds is 17 m/s and after 30 seconds is 583.2 m/s.