The figure shows the velocity of a solar-powered car as a function of time. The driver accelerates from a stop sign, cruises for 20 at a constant speed of 60 , and then brakes to come to a stop 40 after leaving the stop sign.
a) 1.7
b) -1.7
c) 0
d) 0
-1.7 b
Please send complete solution
To analyze the velocity of the solar-powered car as a function of time, we will break down the given information.
1. The car starts from a stop sign, which means initially the velocity is zero.
2. Then the driver accelerates until reaching a constant speed for a given time.
3. After cruising at a constant speed, the driver brakes to bring the car to a stop.
Let's represent the time with the variable 't' and the velocity with the variable 'v(t)'.
1. Initially (t = 0), the velocity is zero. We can represent this as:
v(t) = 0, where t is less than or equal to 0.
2. The driver accelerates from the stop sign until reaching a constant speed of 60 for 20 seconds. The velocity increases during this time:
v(t) = a(t) + v₀, where t is between 0 and 20, a(t) represents the acceleration, and v₀ represents the initial velocity at t = 0.
3. After cruising at a constant speed of 60 for 20 seconds, the driver brakes to bring the car to a stop. The velocity decreases during this time:
v(t) = b(t) + v₁, where t is between 20 and 60, b(t) represents the deceleration, and v₁ represents the final velocity at t = 20.
Combining these three intervals, we can represent the velocity of the car as a piecewise function:
v(t) = 0, t <= 0
v(t) = a(t) + v₀, 0 < t <= 20
v(t) = b(t) + v₁, 20 < t <= 60
v(t) = 0, t > 60
To determine the acceleration (a(t)) and deceleration (b(t)) functions, as well as the initial (v₀) and final velocities (v₁), we need additional data or information provided.