DYNAMICS OF RIGID BODIES - KINEMATICS OF A PARTICLE ERRATIC MOTION.pdf
- 1. KINEMATICS OF A PARTICLE: MOTION CURVES DYNAMICS OF RIGID BODIES
- 2. S-T GRAPH KINEMATICS OF A PARTICLE: ERRATIC MOTION Plots of position vs. time can be used to find velocity vs. time curves. Finding the slope of the line tangent to the motion curve at any point is the velocity at that point or Therefore, v-t graph can be constructed by finding the slope at various points along s-t graph.
- 3. V-T GRAPH KINEMATICS OF A PARTICLE: ERRATIC MOTION Plots of velocity vs. time can be used to find acceleration vs. time curves. Finding the slope of the line tangent to the velocity curve at any point is the acceleration at that point or Therefore, the a-t graph can be constructed by finding the slope at various points along the v-t graph. Also, the distance moved (displacement) of the particle is the area under the v-t graph during time ∆𝑡.
- 4. A-T GRAPH KINEMATICS OF A PARTICLE: ERRATIC MOTION Given the a-t curve, the change in velocity (∆𝑣) during a time period is the area under the a-t curve. So we can construct a v-t graph from an a-t graph if we know the initial velocity of the particle.
- 5. A-S GRAPH KINEMATICS OF A PARTICLE: ERRATIC MOTION The area under the acceleration versus position curve represents the change in velocity. (recall 𝑎𝑑𝑠 = 𝑣𝑑𝑣). This equation can be solved for 𝑣1, allowing you to solve for the velocity at a point. By doing this repeatedly, you can create a plot of velocity versus distance.
- 6. V-S AND A-S GRAPH KINEMATICS OF A PARTICLE: ERRATIC MOTION By reading the velocity v at a point on the curve and multiplying it by the slope of the curve (dv/ds) at this same point, we can obtain the acceleration at that point.
- 7. V-S AND A-S GRAPH KINEMATICS OF A PARTICLE: ERRATIC MOTION If the a–s graph can be constructed, then points on the v-s graph can be determined by using v dv = a ds. Integrating this equation between the limits v = v0 at s = s0 and v = v1 at s = s1 , we have,
- 8. KINEMATICS OF A PARTICLE: ERRATIC MOTION
- 9. KINEMATICS OF A PARTICLE: ERRATIC MOTION
- 10. EXAMPLE 1 A bicycle moves along a straight road such that its position is described by the graph shown in figure. Construct the v-t and a-t graphs for 0 ≤ 𝑡 ≤ 30 𝑠. KINEMATICS OF A PARTICLE: ERRATIC MOTION
- 11. EXAMPLE 1 A bicycle moves along a straight road such that its position is described by the graph shown in figure. Construct the v-t and a-t graphs for 0 ≤ 𝑡 ≤ 30 𝑠. KINEMATICS OF A PARTICLE: ERRATIC MOTION