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By A. E. H. LOVE

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Extra resources for A TREATISE ON THE MATHEMATICAL THEORY OF ELASTICITY VOLUME-1

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SET UP: Assume the ball moves in the + x direction. 0 ms . 14 m/s − 0 = = 2440 m/s 2 . 25. 10 m , which agrees with our previous result. The acceleration of the ball is very large. IDENTIFY: Assume that the acceleration is constant and apply the constant acceleration kinematic equations. Set ax equal to its maximum allowed value. SET UP: Let + x be the direction of the initial velocity of the car. ax = −250 m/s 2 . 17 m/s . 70 m . 2ax 2(−250 m/s 2 ) EVALUATE: The car frame stops over a shorter distance and has a larger magnitude of acceleration.

D) The cars have the same velocity when their x-t graphs have the same slope. This occurs at approximately t=2s. (e) Car A passes car B when x A moves above xB in the x-t graph. This happens at t = 3 s . 35 (f) Car B passes car A when xB moves above x A in the x-t graph. This happens at t = 1 s . EVALUATE: When ax = 0 , the graph of vx versus t is a horizontal line. When ax is positive, the graph of vx versus t is a straight line with positive slope. 36. IDENTIFY: Apply the constant acceleration equations to the motion of each vehicle.

28. 28 × 10 m . 2 2 ⎝ ⎠ ⎝ ⎠ EVALUATE: When the acceleration is constant the instantaneous acceleration throughout the time interval equals the average acceleration for that time interval. 00 s) 2 = 179 m , which agrees with our previous calculation. IDENTIFY: Apply the constant acceleration kinematic equations to the motion of the car. 250 mi = 1320 ft . 0 ft/s . Let + x be the direction the car is traveling. 0 ft/s , x − x0 = 146 ft , vx = 0 . 9 s . 5 ft/s 2 EVALUATE: The magnitude of the acceleration while braking is much larger than when speeding up.

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A TREATISE ON THE MATHEMATICAL THEORY OF ELASTICITY VOLUME-1 by A. E. H. LOVE


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