Опция с data.table
library(data.table)
i1 <- setDT(df)[, .I[which(Threshold == 1)[1]], Car]$V1
df[i1, .(Value = MPH, Car)]
# Value Car
#1: 32 A
#2: 34 B
data
df <- structure(list(MPH = c(30L, 31L, 32L, 33L, 34L, 35L, 30L, 31L,
32L, 33L, 34L, 35L), Threshold = c(0L, 0L, 1L, 1L, 1L, 1L, 0L,
0L, 0L, 0L, 1L, 1L), Car = c("A", "A", "A", "A", "A", "A", "B",
"B", "B", "B", "B", "B")), class = "data.frame", row.names = c(NA,
-12L))