- #1
Adriano25
- 40
- 4
I've made a drawing in order to visualize the problem better:
1. Homework Statement
A car can increase its speed only at 3.00 m/s2, move at constant velocity, or decrease its speed at 7.00 m/s2. Starting at rest, the driver wishes to drive to a road sign located at x=100 m. He increases his speed, then travels at constant velocity and then decreasing his speed.
The driver begins accelerating at t=0 and switches to constant velocity at t=4.50 s. At what position must the driver switch from constant velocity to decreasing speed if he wants to stop the car at the road sign?
These are the kinematic equations I used to solve the problem:
x1=x0+v0(t1-t0) + 1/2a0(t1-t0)2
v1=v0+a0(t1-t0)
v32=v22 + 2a2(x3-x2)
x1=x0+v0(t1-t0) + 1/2a0(t1-t0)2
x1=1/2a0t12 =
x1=1/2(3.0m/s2)(4.50s)2 = 30.4m
v1=v0+a0(t1-t0)
v1=(3.0m/s2)(4.50s) = 13.5m/s
Since after v1 the velocity is constant, v2 must be constant and equal to 13.5m/s
v32=v22 + 2a2(x3-x2)
-v22=2a2x3-2a2x2
x2=-[-(v22-2a2x3) / 2a2]
x2 = -[(-182.25+1400)/-14] = 86.98m
Does this result look right?
1. Homework Statement
A car can increase its speed only at 3.00 m/s2, move at constant velocity, or decrease its speed at 7.00 m/s2. Starting at rest, the driver wishes to drive to a road sign located at x=100 m. He increases his speed, then travels at constant velocity and then decreasing his speed.
The driver begins accelerating at t=0 and switches to constant velocity at t=4.50 s. At what position must the driver switch from constant velocity to decreasing speed if he wants to stop the car at the road sign?
Homework Equations
These are the kinematic equations I used to solve the problem:
x1=x0+v0(t1-t0) + 1/2a0(t1-t0)2
v1=v0+a0(t1-t0)
v32=v22 + 2a2(x3-x2)
The Attempt at a Solution
x1=x0+v0(t1-t0) + 1/2a0(t1-t0)2
x1=1/2a0t12 =
x1=1/2(3.0m/s2)(4.50s)2 = 30.4m
v1=v0+a0(t1-t0)
v1=(3.0m/s2)(4.50s) = 13.5m/s
Since after v1 the velocity is constant, v2 must be constant and equal to 13.5m/s
v32=v22 + 2a2(x3-x2)
-v22=2a2x3-2a2x2
x2=-[-(v22-2a2x3) / 2a2]
x2 = -[(-182.25+1400)/-14] = 86.98m
Does this result look right?