Let the first acceleration be a1=2.5m/s2 and the second one a2=3m/s2. The Initial speed is v0=0, the next one is v1=12.5m/s and the final is v2=0. The total distance is d=1km=1000m.
Let's find the time t1 of the first acceleration from v0 to v1
By definition, the acceleration is:
a1=t1v1−v0t1=a1v1−v0=2.512.5−0=5s During this time the car covered the distance:
d1=2a1t12=22.5⋅52=31.25m Let's find the time t3 of the last acceleration. Again, by definition:
a2=t3v2−v1t1=a2∣v2−v1∣=3∣0−12.5∣=625s During this time the car covered the distance:
d3=2a2t32=2⋅623⋅252=156.25m The distance in the middle, covered with a constant speed v1 is then:
d2=d−d1−d3=1000m−31.25m−156.25m=812.5m Thus, the time during which it was covered is:
t2=d2/v1=65s Thus, the total time is:
t=t1+t2+t3=5s+625s+65s≈74.17s Answer. 74.17s.
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