Physics help, show all work Vav = ½ ( vo + v ); x = xo + vot + ½ a t2 ; 1 mile =
ID: 1532856 • Letter: P
Question
Physics help, show all work
Vav = ½ ( vo + v ); x = xo + vot + ½ a t2 ; 1 mile = 5280 ft = 1.609 km
a = (V - Vo) / t ; x = Vav . T ; 1 in = 2.54 cm, 1ft = 0.3048 m
A motorist is driving at a steady 45 m/s. 35 seconds later he noticies the police ahead so he slows down to 30 m/s taking 15 sec to do so. He then continues driving at 30 m/s for 40 s then takes 25 s to bring the car to a stop as he had reached his destination. (hint: draw a graph of speed vs time)
(i) Calculate the total distance traveled.
(ii) Calculate the deceleration (negative acceleration) that brought the car to a stop.
(iii) Calculate the average speed for the entire period.
Explanation / Answer
Break motorist path in 4 parts
Path 1 = 45m/s for 35 seconds
Distance x1 = 45x35 = 1575 m
Path 2 = 45m/s to 30m/s in 15 seconds
Vav = (45+30)/2 m/s
Distance x2 = (75/2)*15 = 562.5 m
Path 3 = 30m/s for 40 seconds
Distance x3 = 30 x 40 = 1200 m
Path 4: deceleration for 25s
a = (-30)/25 = 1.2 m/s2
distance x4 = 30x25 – 0.5x1.2x25x25 = 375m
(a)Total distance = 1575 +562.5 + 1200 +375 = 3712.5 m
(b) deceleration = 1.2 m/s2
(c) average speed = total distance/total time = 3712.5/115 = 32.28 m/s